Patent

From Wikipedia, the free encyclopedia

U.S. patent

A patent is a form of intellectual property. A patent gives its owner the right to exclude others from making, using, selling, and importing an invention for a limited period of time, usually twenty years. The patent rights are granted in exchange for an enabling public disclosure of the invention. In most countries patent rights fall under civil law and the patent holder needs to sue someone infringing the patent in order to enforce their rights. In some industries patents are an essential form of competitive advantage; in others they are irrelevant.

The procedure for granting patents, requirements placed on the patentee, and the extent of the exclusive rights vary widely between countries according to national laws and international agreements. Typically, however, a granted patent application must include one or more claims that define the invention. A patent may include many claims, each of which defines a specific property right. These claims must meet relevant patentability requirements, such as novelty, usefulness, and non-obviousness.

Under the World Trade Organization's (WTO) TRIPS Agreement, patents should be available in WTO member states for any invention, in all fields of technology, provided they are new, involve an inventive step, and are capable of industrial application. Nevertheless, there are variations on what is patentable subject matter from country to country, also among WTO member states. TRIPS also provides that the term of protection available should be a minimum of twenty years.

Definition

The word patent originates from the Latin patere, which means "to lay open" (i.e., to make available for public inspection). It is a shortened version of the term letters patent, which was an open document or instrument issued by a monarch or government granting exclusive rights to a person, predating the modern patent system. Similar grants included land patents, which were land grants by early state governments in the USA, and printing patents, a precursor of modern copyright.

In modern usage, the term patent usually refers to the right granted to anyone who invents something new, useful and non-obvious. Some other types of intellectual property rights are also called patents in some jurisdictions: industrial design rights are called design patents in the US, plant breeders' rights are sometimes called plant patents, and utility models and Gebrauchsmuster are sometimes called petty patents or innovation patents.

The additional qualification utility patent is sometimes used (primarily in the US) to distinguish the primary meaning from these other types of patents. Particular species of patents for inventions include biological patents, business method patents, chemical patents and software patents.

History

The Venetian Patent Statute, issued by the Senate of Venice in 1474, and one of the earliest statutory patent systems in the world.

 

Although there is some evidence that some form of patent rights was recognized in Ancient Greece in the Greek city of Sybaris, the first statutory patent system is generally regarded to be the Venetian Patent Statute of 1474. Patents were systematically granted in Venice as of 1474, where they issued a decree by which new and inventive devices had to be communicated to the Republic in order to obtain legal protection against potential infringers. The period of protection was 10 years. As Venetians emigrated, they sought similar patent protection in their new homes. This led to the diffusion of patent systems to other countries.

The English patent system evolved from its early medieval origins into the first modern patent system that recognized intellectual property in order to stimulate invention; this was the crucial legal foundation upon which the Industrial Revolution could emerge and flourish. By the 16th century, the English Crown would habitually abuse the granting of letters patent for monopolies. After public outcry, King James I of England (VI of Scotland) was forced to revoke all existing monopolies and declare that they were only to be used for "projects of new invention". This was incorporated into the Statute of Monopolies (1624) in which Parliament restricted the Crown's power explicitly so that the King could only issue letters patent to the inventors or introducers of original inventions for a fixed number of years. The Statute became the foundation for later developments in patent law in England and elsewhere. 

James Puckle's 1718 early autocannon was one of the first inventions required to provide a specification for a patent.

 

Important developments in patent law emerged during the 18th century through a slow process of judicial interpretation of the law. During the reign of Queen Anne, patent applications were required to supply a complete specification of the principles of operation of the invention for public access. Legal battles around the 1796 patent taken out by James Watt for his steam engine, established the principles that patents could be issued for improvements of an already existing machine and that ideas or principles without specific practical application could also legally be patented. Influenced by the philosophy of John Locke, the granting of patents began to be viewed as a form of intellectual property right, rather than simply the obtaining of economic privilege. 

The English legal system became the foundation for patent law in countries with a common law heritage, including the United States, New Zealand and Australia. In the Thirteen Colonies, inventors could obtain patents through petition to a given colony's legislature. In 1641, Samuel Winslow was granted the first patent in North America by the Massachusetts General Court for a new process for making salt.

U.S. patents granted, 1790–2010.

 

The modern French patent system was created during the Revolution in 1791. Patents were granted without examination since inventor's right was considered as a natural one. Patent costs were very high (from 500 to 1,500 francs). Importation patents protected new devices coming from foreign countries. The patent law was revised in 1844 - patent cost was lowered and importation patents were abolished. 

The first Patent Act of the U.S. Congress was passed on April 10, 1790, titled "An Act to promote the progress of useful Arts". The first patent was granted on July 31, 1790 to Samuel Hopkins for a method of producing potash (potassium carbonate). A revised patent law was passed in 1793, and in 1836 a major revision to the patent law was passed. The 1836 law instituted a significantly more rigorous application process, including the establishment of an examination system. Between 1790 and 1836 about ten thousand patents were granted. By the Civil War about 80,000 patents had been granted.

Law

Effects

A patent does not give a right to make or use or sell an invention. Rather, a patent provides, from a legal standpoint, the right to exclude others from making, using, selling, offering for sale, or importing the patented invention for the term of the patent, which is usually 20 years from the filing date subject to the payment of maintenance fees. From an economic and practical standpoint however, a patent is better and perhaps more precisely regarded as conferring upon its proprietor "a right to try to exclude by asserting the patent in court", for many granted patents turn out to be invalid once their proprietors attempt to assert them in court. A patent is a limited property right the government gives inventors in exchange for their agreement to share details of their inventions with the public. Like any other property right, it may be sold, licensed, mortgaged, assigned or transferred, given away, or simply abandoned.

A patent, being an exclusionary right, does not necessarily give the patent owner the right to exploit the invention subject to the patent. For example, many inventions are improvements of prior inventions that may still be covered by someone else's patent. If an inventor obtains a patent on improvements to an existing invention which is still under patent, they can only legally use the improved invention if the patent holder of the original invention gives permission, which they may refuse. 

Some countries have "working provisions" that require the invention be exploited in the jurisdiction it covers. Consequences of not working an invention vary from one country to another, ranging from revocation of the patent rights to the awarding of a compulsory license awarded by the courts to a party wishing to exploit a patented invention. The patentee has the opportunity to challenge the revocation or license, but is usually required to provide evidence that the reasonable requirements of the public have been met by the working of invention.

Challenges

In most jurisdictions, there are ways for third parties to challenge the validity of an allowed or issued patent at the national patent office; these are called opposition proceedings. It is also possible to challenge the validity of a patent in court. In either case, the challenging party tries to prove that the patent should never have been granted. There are several grounds for challenges: the claimed subject matter is not patentable subject matter at all; the claimed subject matter was actually not new, or was obvious to experts in the field, at the time the application was filed; or that some kind of fraud was committed during prosecution with regard to listing of inventors, representations about when discoveries were made, etc. Patents can be found to be invalid in whole or in part for any of these reasons.

Infringement

Patent infringement occurs when a third party, without authorization from the patentee, makes, uses, or sells a patented invention. Patents, however, are enforced on a nation by nation basis. The making of an item in China, for example, that would infringe a U.S. patent, would not constitute infringement under US patent law unless the item were imported into the US.

Enforcement

Patents can generally only be enforced through civil lawsuits (for example, for a U.S. patent, by an action for patent infringement in a United States federal court), although some countries (such as France and Austria) have criminal penalties for wanton infringement. Typically, the patent owner seeks monetary compensation for past infringement, and seeks an injunction that prohibits the defendant from engaging in future acts of infringement. To prove infringement, the patent owner must establish that the accused infringer practises all the requirements of at least one of the claims of the patent. (In many jurisdictions the scope of the patent may not be limited to what is literally stated in the claims, for example due to the doctrine of equivalents). 

An accused infringer has the right to challenge the validity of the patent allegedly being infringed in a counterclaim. A patent can be found invalid on grounds described in the relevant patent laws, which vary between countries. Often, the grounds are a subset of requirements for patentability in the relevant country. Although an infringer is generally free to rely on any available ground of invalidity (such as a prior publication, for example), some countries have sanctions to prevent the same validity questions being relitigated. An example is the UK Certificate of contested validity. 

Patent licensing agreements are contracts in which the patent owner (the licensor) agrees to grant the licensee the right to make, use, sell, and/or import the claimed invention, usually in return for a royalty or other compensation. It is common for companies engaged in complex technical fields to enter into multiple license agreements associated with the production of a single product. Moreover, it is equally common for competitors in such fields to license patents to each other under cross-licensing agreements in order to share the benefits of using each other's patented inventions.

Ownership

In most countries, both natural persons and corporate entities may apply for a patent. In the United States, however, only the inventor(s) may apply for a patent although it may be assigned to a corporate entity subsequently and inventors may be required to assign inventions to their employers under an employment contract. In most European countries, ownership of an invention may pass from the inventor to their employer by rule of law if the invention was made in the course of the inventor's normal or specifically assigned employment duties, where an invention might reasonably be expected to result from carrying out those duties, or if the inventor had a special obligation to further the interests of the employer's company.

The plate of the Martin ejector seat of a military aircraft, stating that the product is covered by multiple patents in the UK, South Africa, Canada and pending in "other" jurisdictions. Dübendorf Museum of Military Aviation.

 

The inventors, their successors or their assignees become the proprietors of the patent when and if it is granted. If a patent is granted to more than one proprietor, the laws of the country in question and any agreement between the proprietors may affect the extent to which each proprietor can exploit the patent. For example, in some countries, each proprietor may freely license or assign their rights in the patent to another person while the law in other countries prohibits such actions without the permission of the other proprietor(s). 

The ability to assign ownership rights increases the liquidity of a patent as property. Inventors can obtain patents and then sell them to third parties. The third parties then own the patents and have the same rights to prevent others from exploiting the claimed inventions, as if they had originally made the inventions themselves.

Governing laws

The grant and enforcement of patents are governed by national laws, and also by international treaties, where those treaties have been given effect in national laws. Patents are granted by national or regional patent offices. A given patent is therefore only useful for protecting an invention in the country in which that patent is granted. In other words, patent law is territorial in nature. When a patent application is published, the invention disclosed in the application becomes prior art and enters the public domain (if not protected by other patents) in countries where a patent applicant does not seek protection, the application thus generally becoming prior art against anyone (including the applicant) who might seek patent protection for the invention in those countries. 

Commonly, a nation or a group of nations forms a patent office with responsibility for operating that nation's patent system, within the relevant patent laws. The patent office generally has responsibility for the grant of patents, with infringement being the remit of national courts. 

The authority for patent statutes in different countries varies. In the UK, substantive patent law is contained in the Patents Act 1977 as amended. In the United States, the Constitution empowers Congress to make laws to "promote the Progress of Science and useful Arts..." The laws Congress passed are codified in Title 35 of the United States Code and created the United States Patent and Trademark Office.

There is a trend towards global harmonization of patent laws, with the World Trade Organization (WTO) being particularly active in this area. The TRIPS Agreement has been largely successful in providing a forum for nations to agree on an aligned set of patent laws. Conformity with the TRIPS agreement is a requirement of admission to the WTO and so compliance is seen by many nations as important. This has also led to many developing nations, which may historically have developed different laws to aid their development, enforcing patents laws in line with global practice.

Internationally, there are international treaty procedures, such as the procedures under the European Patent Convention (EPC) [constituting the European Patent Organisation (EPOrg)], that centralize some portion of the filing and examination procedure. Similar arrangements exist among the member states of ARIPO and OAPI, the analogous treaties among African countries, and the nine CIS member states that have formed the Eurasian Patent Organization. A key international convention relating to patents is the Paris Convention for the Protection of Industrial Property, initially signed in 1883. The Paris Convention sets out a range of basic rules relating to patents, and although the convention does not have direct legal effect in all national jurisdictions, the principles of the convention are incorporated into all notable current patent systems. The most significant aspect of the convention is the provision of the right to claim priority: filing an application in any one member state of the Paris Convention preserves the right for one year to file in any other member state, and receive the benefit of the original filing date. Another key treaty is the Patent Cooperation Treaty (PCT), administered by WIPO and covering more than 150 countries. The Patent Cooperation Treaty provides a unified procedure for filing patent applications to protect inventions in each of its contracting states. A patent application filed under the PCT is called an international application, or PCT application.

Application and prosecution

A patent is requested by filing a written application at the relevant patent office. The person or company filing the application is referred to as "the applicant". The applicant may be the inventor or its assignee. The application contains a description of how to make and use the invention that must provide sufficient detail for a person skilled in the art (i.e., the relevant area of technology) to make and use the invention. In some countries there are requirements for providing specific information such as the usefulness of the invention, the best mode of performing the invention known to the inventor, or the technical problem or problems solved by the invention. Drawings illustrating the invention may also be provided. 

The application also includes one or more claims that define what a patent covers or the "scope of protection". 

After filing, an application is often referred to as "patent pending". While this term does not confer legal protection, and a patent cannot be enforced until granted, it serves to provide warning to potential infringers that if the patent is issued, they may be liable for damages.

Once filed, a patent application is "prosecuted". A patent examiner reviews the patent application to determine if it meets the patentability requirements of that country. If the application does not comply, objections are communicated to the applicant or their patent agent or attorney through an Office action, to which the applicant may respond. The number of Office actions and responses that may occur vary from country to country, but eventually a final rejection is sent by the patent office, or the patent application is granted, which after the payment of additional fees, leads to an issued, enforceable patent. In some jurisdictions, there are opportunities for third parties to bring an opposition proceeding between grant and issuance, or post-issuance.

Once granted the patent is subject in most countries to renewal fees to keep the patent in force. These fees are generally payable on a yearly basis. Some countries or regional patent offices (e.g. the European Patent Office) also require annual renewal fees to be paid for a patent application before it is granted.

Costs

The costs of preparing and filing a patent application, prosecuting it until grant and maintaining the patent vary from one jurisdiction to another, and may also be dependent upon the type and complexity of the invention, and on the type of patent.

The European Patent Office estimated in 2005 that the average cost of obtaining a European patent (via a Euro-direct application, i.e. not based on a PCT application) and maintaining the patent for a 10-year term was around €32,000. Since the London Agreement entered into force on May 1, 2008, this estimation is however no longer up-to-date, since fewer translations are required.

In the United States, in 2000 the cost of obtaining a patent (patent prosecution) was estimated to be from $10,000 to $30,000 per patent. When patent litigation is involved (which in year 1999 happened in about 1,600 cases compared to 153,000 patents issued in the same year), costs increase significantly: although 95% of patent litigation cases are settled out of court, those that reach the courts have legal costs on the order of a million dollars per case, not including associated business costs.

Alternatives

A defensive publication is the act of publishing a detailed description of a new invention without patenting it, so as to establish prior art and public identification as the creator/originator of an invention, although a defensive publication can also be anonymous. A defensive publication prevents others from later being able to patent the invention.

A trade secret is information that is intentionally kept confidential and that provides a competitive advantage to its possessor. Trade secrets are protected by non-disclosure agreement and labor law, each of which prevents information leaks such as breaches of confidentiality and industrial espionage. Compared to patents, the advantages of trade secrets are that the value of a trade secret continues until it is made public, whereas a patent is only in force for a specified time, after which others may freely copy the invention; does not require payment of fees to governmental agencies or filing paperwork; has an immediate effect; and does not require any disclosure of information to the public. The key disadvantage of a trade secret is its vulnerability to reverse engineering.

Benefits

Primary incentives embodied in the patent system include incentives to invent in the first place; to disclose the invention once made; to invest the sums necessary to experiment, produce and market the invention; and to design around and improve upon earlier patents.

• Patents provide incentives for economically efficient research and development (R&D). A study conducted annually by the Institute for Prospective Technological Studies (IPTS) shows that the 2,000 largest global companies invested more than 430 billion euros in 2008 in their R&D departments. If the investments can be considered as inputs of R&D, real products and patents are the outputs. Based on these groups, a project named Corporate Invention Board, had measured and analyzed the patent portfolios to produce an original picture of their technological profiles. Supporters of patents argue that without patent protection, R&D spending would be significantly less or eliminated altogether, limiting the possibility of technological advances or breakthroughs. Corporations would be much more conservative about the R&D investments they made, as third parties would be free to exploit any developments. This second justification is closely related to the basic ideas underlying traditional property rights. Specifically, "[t]he patent internalizes the externality by giving the [inventor] a property right over its invention." A 2008 study by Yi Quan of Kellogg School of Management showed that countries instituting patent protection on pharmaceuticals did not necessarily have an increase in domestic pharmaceutical innovation. Only countries with "higher levels of economic development, educational attainment, and economic freedom" showed an increase. There also appeared to be an optimal level of patent protection that increased domestic innovation.
• In accordance with the original definition of the term "patent", patents are intended to facilitate and encourage disclosure of innovations into the public domain for the common good. Thus patenting can be viewed as contributing to open hardware after an embargo period (usually of 20 years). If inventors did not have the legal protection of patents, in many cases, they might prefer or tend to keep their inventions secret (e.g. keep trade secrets). Awarding patents generally makes the details of new technology publicly available, for exploitation by anyone after the patent expires, or for further improvement by other inventors. Furthermore, when a patent's term has expired, the public record ensures that the patentee's invention is not lost to humanity.
• In many industries (especially those with high fixed costs and either low marginal costs or low reverse engineering costs — computer processors, and pharmaceuticals for example), once an invention exists, the cost of commercialization (testing, tooling up a factory, developing a market, etc.) is far more than the initial conception cost. (For example, the internal rule of thumb at several computer companies in the 1980s was that post-R&D costs were 7-to-1.)

One effect of modern patent usage is that a small-time inventor, who can afford both the patenting process and the defense of the patent, can use the exclusive right status to become a licensor. This allows the inventor to accumulate capital from licensing the invention and may allow innovation to occur because he or she may choose not to manage a manufacturing buildup for the invention. Thus the inventor's time and energy can be spent on pure innovation, allowing others to concentrate on manufacturability.

Another effect of modern patent usage is to both enable and incentivize competitors to design around (or to "invent around" according to R S Praveen Raj) the patented invention. This may promote healthy competition among manufacturers, resulting in gradual improvements of the technology base. This may help augment national economies and confer better living standards to the citizens. The 1970 Indian Patent Act allowed the Indian pharmaceutical industry to develop local technological capabilities in this industry. This act coincided with the transformation of India from a bulk importer of pharmaceutical drugs to a leading exporter. The rapid evolution of Indian pharmaceutical industry since the mid-1970s highlights the fact that the design of the patent act was instrumental in building local capabilities even in a developing country like India.

Criticism

Legal scholars, economists, activists, policymakers, industries, and trade organizations have held differing views on patents and engaged in contentious debates on the subject. Critical perspectives emerged in the nineteenth century that were especially based on the principles of free trade. Contemporary criticisms have echoed those arguments, claiming that patents block innovation and waste resources (e.g. with patent-related overheads) that could otherwise be used productively to improve technology. These and other research findings that patents decreased innovation because of the following mechanisms:

• Low quality, already known or obvious patents hamper innovation and commercialization.
• Blocking the use of fundamental knowledge with patents creates a "tragedy of the anticommons, where future innovations can not take place outside of a single firm in an entire field.
• Patents weaken the public domain and innovation that comes from it.
• Patent thickets, or "an overlapping set of patent rights", in particular slow innovation.
• Broad patents prevent companies from commercializing products and hurt innovation. In the worst case, such broad patents are held by non-practicing entities (patent trolls), which do not contribute to innovation. Enforcement by patent trolls of poor quality patents  has led to criticism of the patent office as well as the system itself. For example, in 2011, United States business entities incurred $29 billion in direct costs because of patent trolls. Lawsuits brought by "patent assertion companies" made up 61% of all patent cases in 2012, according to the Santa Clara University School of Law.
• Patents apply a "one size fits all" model to industries with differing needs, that is especially unproductive for the software industry.
• Rent-seeking by owners of pharmaceutical patents have also been a particular focus of criticism, as the high prices they enable puts life-saving drugs out of reach of many people.

Boldrin and Levine conclude "Our preferred policy solution is to abolish patents entirely and to find other legislative instruments, less open to lobbying and rent seeking, to foster innovation when there is clear evidence that laissez-faire undersupplies it." Abolishing patents may be politically challenging in some countries, however, as the primary economic theories supporting patent law hold that inventors and innovators need patents to recoup the costs associated with research, inventing, and commercializing; this reasoning is weakened if the new technologies decrease these costs. A 2016 paper argued for substantial weakening of patents because current technologies (e.g. 3D printing, cloud computing, synthetic biology, etc.) have reduced the cost of innovation.

Debates over the usefulness of patents for their primary objective are part of a larger discourse on intellectual property protection, which also reflects differing perspectives on copyright.

Anti-patent initiatives

• The Patent Busting Project is an Electronic Frontier Foundation (EFF) initiative challenging patents that the organization claims are illegitimate and suppress innovation or limit online expression. The initiative launched in 2004 and involves two phases: documenting the damage caused by these patents^{[citation needed]}, and submitting challenges to the United States Patent and Trademark Office (USPTO).
• Patent critic, Joseph Stiglitz has proposed Prizes as an alternative to patents in order to further advance solutions to global problems such as AIDS.
• In 2012, Stack Exchange launched Ask Patents, a forum for crowdsourcing prior art to invalidate patents.
• Several authors have argued for developing defensive prior art to prevent patenting based on obviousness using lists or algorithms. For example, a Professor of Law at the University of North Carolina School of Law, has demonstrated a method to protect DNA research., which could apply to other technology. Chin wrote an algorithm to generate 11 million "obvious" nucleotide sequences to count as prior art and his algorithmic approach has already proven effective at anticipating prior art against oligonucleotide composition claims filed since his publication of the list and has been cited by the U.S. patent office a number of times. More recently, Joshua Pearce developed an open-source algorithm for identifying prior art for 3D printing materials to make such materials obvious by patent standards. As the 3-D printing community is already grappling with legal issues, this development was hotly debated in the technical press. Chin made the same algorithem-based obvious argument in DNA probes.
• Google and other technology companies founded the LOT Network in 2014 to combat patent assertion entities by cross-licensing patents, thereby preventing legal action by such entities.

History of perpetual motion machines

From Wikipedia, the free encyclopedia

An engraving of Robert Fludd's 1618 "water screw" perpetual motion machine.

 

The history of perpetual motion machines dates at least back to the Middle Ages. For millennia, it was not clear whether perpetual motion devices were possible or not, but modern theories of thermodynamics have shown that they are impossible. Despite this, many attempts have been made to construct such machines, continuing into modern times. Modern designers and proponents sometimes use other terms, such as "overunity", to describe their inventions.

History

Kinds of perpetual motion machines

Perpetuum Mobile of Villard de Honnecourt (about 1230) 15th-century wheel by Taccola Orffyreus' Mersseburgische Perpetuum Mobile Boyle's perpetual motion scheme

There are two types of perpetual motion machines: Perpetual motion machines of the first kind are those devices that violate the first law of thermodynamics, the principle of conservation of energy, creating energy out of nothing. Most attempts fall into this category. Perpetual motion machines of the second kind are devices that violate the second law of thermodynamics. Even though they obey the principle of conservation of energy, they attempt extraction of work from a single heat reservoir, violating the principle of no entropy decrease in an isolated macroscopic thermodynamic system.

Pre-19th century

There are some unsourced claims that a perpetual motion machine called the "magic wheel" (a wheel spinning on its axle powered by lodestones) appeared in 8th-century Bavaria. This historical claim appears to be unsubstantiated though often repeated. 

Early designs of perpetual motion machines were done by Indian mathematician–astronomer Bhaskara II, who described a wheel (Bhāskara's wheel) that he claimed would run forever.

A drawing of a perpetual motion machine appeared in the sketchbook of Villard de Honnecourt, a 13th-century French master mason and architect. The sketchbook was concerned with mechanics and architecture. Following the example of Villard, Peter of Maricourt designed a magnetic globe which, if it were mounted without friction parallel to the celestial axis, would rotate once a day. It was intended to serve as an automatic armillary sphere.

Leonardo da Vinci made a number of drawings of devices he hoped would make free energy. Leonardo da Vinci was generally against such devices, but drew and examined numerous overbalanced wheels.

Mark Anthony Zimara, a 16th-century Italian scholar, proposed a self-blowing windmill.

Various scholars in this period investigated the topic. In 1607 Cornelius Drebbel in "Wonder-vondt van de eeuwighe bewegingh" dedicated a Perpetuum motion machine to James I of England. It was described by Heinrich Hiesserle von Chodaw in 1621. Robert Boyle devised the "perpetual vase" ("perpetual goblet" or "hydrostatic paradox") which was discussed by Denis Papin in the Philosophical Transactions for 1685. Johann Bernoulli proposed a fluid energy machine. In 1686, Georg Andreas Böckler, designed a "self operating" self-powered water mill and several perpetual motion machines using balls using variants of Archimedes' screws. In 1712, Johann Bessler (Orffyreus), claimed to have experimented with 300 different perpetual motion models before developing what he said were working models.

In the 1760s, James Cox and John Joseph Merlin developed Cox's timepiece. Cox claimed that the timepiece was a true perpetual motion machine, but as the device is powered by changes in atmospheric pressure via a mercury barometer, this is not the case. 

In 1775, the Royal Academy of Sciences in Paris made the statement that the Academy "will no longer accept or deal with proposals concerning perpetual motion."

Industrial Revolution

19th century

In 1812, Charles Redheffer, in Philadelphia, claimed to have developed a "generator" that could power other machines. The machine was open for viewing in Philadelphia, where Redheffer raised large amount of money from the admission fee. Redheffer moved his machine to New York, after his cover was blown in Philadelphia, while applying for government funding. It was there that Robert Fulton exposed Redheffer's schemes during an exposition of the device in New York City (1813). Removing some concealing wooden strips, Fulton found a catgut belt drive went through a wall to an attic. In the attic, a man was turning a crank to power the device.

In 1827, Sir William Congreve, 2nd Baronet devised a machine running on capillary action that would disobey the principle that water seeks its own level, so to produce a continuous ascent and overflow. The device had an inclined plane over pulleys. At the top and bottom, there travelled an endless band of sponge, a bed and, over this, again an endless band of heavy weights jointed together. The whole stood over the surface of still water. Congreve believed his system would operate continuously.

In 1868, an Austrian, Alois Drasch, received a US patent for a machine that possessed a "thrust key-type gearing" of a rotary engine. The vehicle driver could tilt a trough depending upon need. A heavy ball rolled in a cylindrical trough downward, and, with continuous adjustment of the device's levers and power output, Drasch believed that it would be possible to power a vehicle.

In 1870, E.P. Willis of New Haven, Connecticut made money from a "proprietary" perpetual motion machine. A story of the overcomplicated device with a hidden source of energy appears in the Scientific American article "The Greatest Discovery Ever Yet Made". Investigation into the device eventually found a source of power that drove it.

John Ernst Worrell Keely claimed the invention of an induction resonance motion motor. He explained that he used "etheric technology". In 1872, Keely announced that he had discovered a principle for power production based on the vibrations of tuning forks. Scientists investigated his machine which appeared to run on water, though Keely endeavoured to avoid this. Shortly after 1872, venture capitalists accused Keely of fraud (they lost nearly five million dollars). Keely's machine, it was discovered after his death, was based on hidden air pressure tubes.

1900 to 1950

In 1900, Nikola Tesla claimed to have discovered an abstract principle on which to base a perpetual motion machine of the second kind. No prototype was produced. He wrote:

“

A departure from known methods – possibility of a "self-acting" engine or machine, inanimate, yet capable, like a living being, of deriving energy from the medium – the ideal way of obtaining motive power.

”

David Unaipon, Australian inventor, had a lifelong fascination with perpetual motion. One of his studies on Newtonian mechanics led him to create a shearing machine in 1910 that converted curvilineal motion into straight line movement. The device is the basis of modern mechanical shears.

In the 1910s and 1920s, Harry Perrigo of Kansas City, Missouri, a graduate of MIT, claimed development of a free energy device. Perrigo claimed the energy source was "from thin air" or from aether waves. He demonstrated the device before the Congress of the United States on December 15, 1917. Perrigo had a pending application for the "Improvement in Method and Apparatus for Accumulating and Transforming Ether Electric Energy". Investigators report that his device contained a hidden motor battery.

Cover of the October 1920 issue of Popular Science magazine

 

Popular Science, in the October 1920 issue, published an article on the lure of perpetual motion.

Modern era

1951 to 1980

During the middle of the 20th century, Viktor Schauberger claimed to have discovered some special vortex energy in water. Since his death in 1958, people are still studying his works.

In 1966, Josef Papp (sometimes referred to as Joseph Papp or Joseph Papf) supposedly developed an alternative car engine that used inert gases. He gained a few investors but when the engine was publicly demonstrated, an explosion killed one of the observers and injured two others. Papp blamed the accident on interference by physicist Richard Feynman, who later shared his observations in an article in Laser, the journal of the Southern Californian Skeptics. Papp continued to accept money but never demonstrated another engine. 

On December 20 of 1977, Emil T. Hartman received U.S. Patent 4,215,330 titled "Permanent magnet propulsion system". This device is related to the Simple Magnetic Overunity Toy (SMOT). 

Thesta-Distatica electrical circuit as explained in Potter's "Methernitha Back-Engineered" article.

 

Paul Bauman, a German engineer, developed a machine referred to as the "Testatika" and known as the "Swiss M-L converter" or "Thesta-Distatica".

Guido Franch reportedly had a process of transmuting water molecules into high-octane gasoline compounds (named Mota fuel) that would reduce the price of gasoline to 8 cents per gallon. This process involved a green powder (this claim may be related to the similar ones of John Andrews (1917)). He was brought to court for fraud in 1954 and acquitted, but in 1973 was convicted. Justice William Bauer and Justice Philip Romiti both observed a demonstration in the 1954 case.

In 1958, Otis T. Carr from Oklahoma formed a company to manufacture UFO-styled spaceships and hovercraft. Carr sold stock for this commercial endeavour. He also promoted free energy machines. He claimed inspiration from Nikola Tesla, among others.

In 1962, physicist Richard Feynman discussed a Brownian ratchet that would supposedly extract meaningful work from Brownian motion, although he went on to demonstrate how such a device would fail to work in practice.

In the 1970s, David Hamel produced the Hamel generator, an "antigravity" device, supposedly after an alien abduction. The device was tested on MythBusters where it failed to demonstrate any lift-generating capability.

Howard R. Johnson's US Patent 4151431

 

Howard Robert Johnson developed a permanent magnet motor and, on April 24, 1979, received U.S. Patent 4,151,431.[The United States Patent office main classification of his 4151431 patent is as a "electrical generator or motor structure, dynamoelectric, linear" (310/12).] Johnson said that his device generates motion, either rotary or linear, from nothing but permanent magnets in rotor as well as stator, acting against each other. He estimated that permanent magnets made of proper hard materials should lose less than two percent of their magnetization in powering a device for 18 years.

In 1979, Joseph Westley Newman applied for a patent on a direct current electrical motor which, according to his book The Energy Machine of Joseph Newman did more mechanical work than could be accounted for by the electrical power supplied to it. Newman's patent application was rejected in 1983. Newman sued the US Patent and Trademark Office in US District Court, which ordered the National Bureau of Standards to test his machine; they informed the Court that Newman's device did not produce more power than supplied by the batteries it was connected to, and the Court found against Newman.

1981 to 1999

Dr. Yuri S. Potapov of Moldova claims development of an over-unity electrothermal water-based generator (referred to as "Yusmar 1"). He founded the YUSMAR company to promote his device. The device has failed to produce over unity under tests.

CETI claimed development of a device that outputs small yet anomalous amounts of heat, perhaps due to cold fusion. Skeptics state that inaccurate measurements of friction effects from the cooling flow through the pellets may be responsible for the results.

2000s

Motionless electromagnetic generator circuit as explained in US Patent 6362718

 

The motionless electromagnetic generator (MEG) was built by Tom Bearden. Allegedly, the device can eventually sustain its operation in addition to powering a load without application of external electrical power. Bearden claimed that it didn't violate the first law of thermodynamics because it extracted vacuum energy from the immediate environment. Critics dismiss this theory and instead identify it as a perpetual motion machine with an unscientific rationalization. Science writer Martin Gardner said that Bearden's physics theories, compiled in the self-published book Energy from the Vacuum, are considered "howlers" by physicists, and that his doctorate title was obtained from a diploma mill. Bearden then founded and directed the Alpha Foundation's Institute for Advanced Study (AIAS) to further propagate his theories. This group has published papers in established physics journals and in books published by leading publishing houses, but one analysis lamented these publications because the texts were "full of misconceptions and misunderstandings concerning the theory of the electromagnetic field." When Bearden was awarded U.S. Patent 6,362,718 in 2002, the American Physical Society issued a statement against the granting. The United States Patent and Trademark Office said that it would reexamine the patent and change the way it recruits examiners, and re-certify examiners on a regular basis, to prevent similar patents from being granted again.

In 2002, the GWE (Genesis World Energy) group claimed to have 400 people developing a device that supposedly separated water into H₂ and O₂ using less energy than conventionally thought possible. No independent confirmation was ever made of their claims, and in 2006, company founder Patrick Kelly was sentenced to five years in prison for stealing funds from investors.

In 2006, Steorn Ltd. claimed to have built an over-unity device based on rotating magnets, and took out an advertisement soliciting scientists to test their claims. The selection process for twelve began in September 2006 and concluded in December 2006. The selected jury started investigating Steorn's claims. A public demonstration scheduled for July 4, 2007 was canceled due to "technical difficulties". In June 2009, the selected jury said the technology does not work.

First law of thermodynamics

From Wikipedia, the free encyclopedia

The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. The first law is often formulated

${\displaystyle \Delta U=Q-W.}$

It states that the change in the internal energy ΔU of a closed system is equal to the amount of heat Q supplied to the system, minus the amount of work W done by the system on its surroundings. An equivalent statement is that perpetual motion machines of the first kind are impossible.

History

Investigations into the nature of heat and work and their relationship began with the invention of the first engines used to extract water from mines. Improvements to such engines so as to increase their efficiency and power output came first from mechanics that worked with such machines but only slowly advanced the art. Deeper investigations that placed those on a mathematical and physics basis came later.

The first law of thermodynamics was developed empirically over about half a century. The first full statements of the law came in 1850 from Rudolf Clausius and from William Rankine; Rankine's statement is considered less distinct relative to Clausius'. A main aspect of the struggle was to deal with the previously proposed caloric theory of heat. 

In 1840, Germain Hess stated a conservation law for the so-called 'heat of reaction' for chemical reactions. His law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work. 

According to Truesdell (1980), Julius Robert von Mayer in 1841 made a statement that meant that "in a process at constant pressure, the heat used to produce expansion is universally interconvertible with work", but this is not a general statement of the first law.

Original statements: the "thermodynamic approach"

The original nineteenth century statements of the first law of thermodynamics appeared in a conceptual framework in which transfer of energy as heat was taken as a primitive notion, not defined or constructed by the theoretical development of the framework, but rather presupposed as prior to it and already accepted. The primitive notion of heat was taken as empirically established, especially through calorimetry regarded as a subject in its own right, prior to thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach.

The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850, referred to cyclic thermodynamic processes.

In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is produced.

Clausius also stated the law in another form, referring to the existence of a function of state of the system, the internal energy, and expressed it in terms of a differential equation for the increments of a thermodynamic process. This equation may be described as follows:

In a thermodynamic process involving a closed system, the increment in the internal energy is equal to the difference between the heat accumulated by the system and the work done by it.

Because of its definition in terms of increments, the value of the internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.

The concept of internal energy is considered by Bailyn to be of "enormous interest". Its quantity cannot be immediately measured, but can only be inferred, by differencing actual immediate measurements. Bailyn likens it to the energy states of an atom, that were revealed by Bohr's energy relation hν = E_n'' − E_n'. In each case, an unmeasurable quantity (the internal energy, the atomic energy level) is revealed by considering the difference of measured quantities (increments of internal energy, quantities of emitted or absorbed radiative energy).

Conceptual revision: the "mechanical approach"

In 1907, George H. Bryan wrote about systems between which there is no transfer of matter (closed systems): "Definition. When energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called heat." This definition may be regarded as expressing a conceptual revision, as follows. This was systematically expounded in 1909 by Constantin Carathéodory, whose attention had been drawn to it by Max Born. Largely through Born's influence, this revised conceptual approach to the definition of heat came to be preferred by many twentieth-century writers. It might be called the "mechanical approach".

Energy can also be transferred from one thermodynamic system to another in association with transfer of matter. Born points out that in general such energy transfer is not resolvable uniquely into work and heat moieties. In general, when there is transfer of energy associated with matter transfer, work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer.

The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another adiabatically as work, and that energy can be held as the internal energy of a thermodynamic system. It also postulates that energy can be transferred from one thermodynamic system to another by a path that is non-adiabatic, and is unaccompanied by matter transfer. Initially, it "cleverly" (according to Bailyn) refrains from labelling as 'heat' such non-adiabatic, unaccompanied transfer of energy. It rests on the primitive notion of walls, especially adiabatic walls and non-adiabatic walls, defined as follows. Temporarily, only for purpose of this definition, one can prohibit transfer of energy as work across a wall of interest. Then walls of interest fall into two classes, (a) those such that arbitrary systems separated by them remain independently in their own previously established respective states of internal thermodynamic equilibrium; they are defined as adiabatic; and (b) those without such independence; they are defined as non-adiabatic.

This approach derives the notions of transfer of energy as heat, and of temperature, as theoretical developments, not taking them as primitives. It regards calorimetry as a derived theory. It has an early origin in the nineteenth century, for example in the work of Helmholtz, but also in the work of many others.

Conceptually revised statement, according to the mechanical approach

The revised statement of the first law postulates that a change in the internal energy of a system due to any arbitrary process, that takes the system from a given initial thermodynamic state to a given final equilibrium thermodynamic state, can be determined through the physical existence, for those given states, of a reference process that occurs purely through stages of adiabatic work. 

The revised statement is then

For a closed system, in any arbitrary process of interest that takes it from an initial to a final state of internal thermodynamic equilibrium, the change of internal energy is the same as that for a reference adiabatic work process that links those two states. This is so regardless of the path of the process of interest, and regardless of whether it is an adiabatic or a non-adiabatic process. The reference adiabatic work process may be chosen arbitrarily from among the class of all such processes.

This statement is much less close to the empirical basis than are the original statements, but is often regarded as conceptually parsimonious in that it rests only on the concepts of adiabatic work and of non-adiabatic processes, not on the concepts of transfer of energy as heat and of empirical temperature that are presupposed by the original statements. Largely through the influence of Max Born, it is often regarded as theoretically preferable because of this conceptual parsimony. Born particularly observes that the revised approach avoids thinking in terms of what he calls the "imported engineering" concept of heat engines.

Basing his thinking on the mechanical approach, Born in 1921, and again in 1949, proposed to revise the definition of heat. In particular, he referred to the work of Constantin Carathéodory, who had in 1909 stated the first law without defining quantity of heat. Born's definition was specifically for transfers of energy without transfer of matter, and it has been widely followed in textbooks. Born observes that a transfer of matter between two systems is accompanied by a transfer of internal energy that cannot be resolved into heat and work components. There can be pathways to other systems, spatially separate from that of the matter transfer, that allow heat and work transfer independent of and simultaneous with the matter transfer. Energy is conserved in such transfers.

Description

Cyclic processes

The first law of thermodynamics for a closed system was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. The other way referred to an incremental change in the internal state of the system, and did not expect the process to be cyclic. 

A cyclic process is one that can be repeated indefinitely often, returning the system to its initial state. Of particular interest for single cycle of a cyclic process are the net work done, and the net heat taken in (or 'consumed', in Clausius' statement), by the system. 

In a cyclic process in which the system does net work on its surroundings, it is observed to be physically necessary not only that heat be taken into the system, but also, importantly, that some heat leave the system. The difference is the heat converted by the cycle into work. In each repetition of a cyclic process, the net work done by the system, measured in mechanical units, is proportional to the heat consumed, measured in calorimetric units. 

The constant of proportionality is universal and independent of the system and in 1845 and 1847 was measured by James Joule, who described it as the mechanical equivalent of heat.

Sign conventions

In a non-cyclic process, the change in the internal energy of a system is equal to net energy added as heat to the system minus the net work done by the system, both being measured in mechanical units. Taking ΔU as a change in internal energy, one writes

${\displaystyle \Delta U=Q\,-\,W\,\,\,\,\mathrm {(sign\,convention\,of\,Clausius\,and\,generally\,in\,this\,article)} ,}$

where Q denotes the net quantity of heat supplied to the system by its surroundings and W denotes the net work done by the system. This sign convention is implicit in Clausius' statement of the law given above. It originated with the study of heat engines that produce useful work by consumption of heat. 

Often nowadays, however, writers use the IUPAC convention by which the first law is formulated with work done on the system by its surroundings having a positive sign. With this now often used sign convention for work, the first law for a closed system may be written:

${\displaystyle \Delta U=Q+W\,\,\,\,\mathrm {(sign\,convention\,of\,IUPAC)} .}$

This convention follows physicists such as Max Planck, and considers all net energy transfers to the system as positive and all net energy transfers from the system as negative, irrespective of any use for the system as an engine or other device. 

When a system expands in a fictive quasistatic process, the work done by the system on the environment is the product, P dV,  of pressure, P, and volume change, dV, whereas the work done on the system is  -P dV.  Using either sign convention for work, the change in internal energy of the system is:

${\displaystyle \mathrm {d} U=\delta Q-P\,\mathrm {d} V\,\,\,\,{\text{(quasi-static process)}},}$

where δQ denotes the infinitesimal amount of heat supplied to the system from its surroundings. 

Work and heat are expressions of actual physical processes of supply or removal of energy, while the internal energy U is a mathematical abstraction that keeps account of the exchanges of energy that befall the system. Thus the term heat for Q means "that amount of energy added or removed by conduction of heat or by thermal radiation", rather than referring to a form of energy within the system. Likewise, the term work energy for W means "that amount of energy gained or lost as the result of work". Internal energy is a property of the system whereas work done and heat supplied are not. A significant result of this distinction is that a given internal energy change ΔU can be achieved by, in principle, many combinations of heat and work.

Various statements of the law for closed systems

The law is of great importance and generality and is consequently thought of from several points of view. Most careful textbook statements of the law express it for closed systems. It is stated in several ways, sometimes even by the same author.

For the thermodynamics of closed systems, the distinction between transfers of energy as work and as heat is central and is within the scope of the present article. For the thermodynamics of open systems, such a distinction is beyond the scope of the present article, but some limited comments are made on it in the section below headed 'First law of thermodynamics for open systems'. 

There are two main ways of stating a law of thermodynamics, physically or mathematically. They should be logically coherent and consistent with one another.

An example of a physical statement is that of Planck (1897/1903):

It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.

This physical statement is restricted neither to closed systems nor to systems with states that are strictly defined only for thermodynamic equilibrium; it has meaning also for open systems and for systems with states that are not in thermodynamic equilibrium.

An example of a mathematical statement is that of Crawford (1963):

For a given system we let ΔE ^kin = large-scale mechanical energy, ΔE ^pot = large-scale potential energy, and ΔE ^tot = total energy. The first two quantities are specifiable in terms of appropriate mechanical variables, and by definition

${\displaystyle E^{\mathrm {tot} }=E^{\mathrm {kin} }+E^{\mathrm {pot} }+U\,\,.}$

For any finite process, whether reversible or irreversible,

${\displaystyle \Delta E^{\mathrm {tot} }=\Delta E^{\mathrm {kin} }+\Delta E^{\mathrm {pot} }+\Delta U\,\,.}$

The first law in a form that involves the principle of conservation of energy more generally is

${\displaystyle \Delta E^{\mathrm {tot} }=Q+W\,\,.}$

Here Q and W are heat and work added, with no restrictions as to whether the process is reversible, quasistatic, or irreversible.[Warner, Am. J. Phys., 29, 124 (1961)]

This statement by Crawford, for W, uses the sign convention of IUPAC, not that of Clausius. Though it does not explicitly say so, this statement refers to closed systems, and to internal energy U defined for bodies in states of thermodynamic equilibrium, which possess well-defined temperatures. 

The history of statements of the law for closed systems has two main periods, before and after the work of Bryan (1907), of Carathéodory (1909), and the approval of Carathéodory's work given by Born (1921). The earlier traditional versions of the law for closed systems are nowadays often considered to be out of date. 

Carathéodory's celebrated presentation of equilibrium thermodynamics refers to closed systems, which are allowed to contain several phases connected by internal walls of various kinds of impermeability and permeability (explicitly including walls that are permeable only to heat). Carathéodory's 1909 version of the first law of thermodynamics was stated in an axiom which refrained from defining or mentioning temperature or quantity of heat transferred. That axiom stated that the internal energy of a phase in equilibrium is a function of state, that the sum of the internal energies of the phases is the total internal energy of the system, and that the value of the total internal energy of the system is changed by the amount of work done adiabatically on it, considering work as a form of energy. That article considered this statement to be an expression of the law of conservation of energy for such systems. This version is nowadays widely accepted as authoritative, but is stated in slightly varied ways by different authors. 

Such statements of the first law for closed systems assert the existence of internal energy as a function of state defined in terms of adiabatic work. Thus heat is not defined calorimetrically or as due to temperature difference. It is defined as a residual difference between change of internal energy and work done on the system, when that work does not account for the whole of the change of internal energy and the system is not adiabatically isolated.

The 1909 Carathéodory statement of the law in axiomatic form does not mention heat or temperature, but the equilibrium states to which it refers are explicitly defined by variable sets that necessarily include "non-deformation variables", such as pressures, which, within reasonable restrictions, can be rightly interpreted as empirical temperatures, and the walls connecting the phases of the system are explicitly defined as possibly impermeable to heat or permeable only to heat.

According to Münster (1970), "A somewhat unsatisfactory aspect of Carathéodory's theory is that a consequence of the Second Law must be considered at this point [in the statement of the first law], i.e. that it is not always possible to reach any state 2 from any other state 1 by means of an adiabatic process." Münster instances that no adiabatic process can reduce the internal energy of a system at constant volume. Carathéodory's paper asserts that its statement of the first law corresponds exactly to Joule's experimental arrangement, regarded as an instance of adiabatic work. It does not point out that Joule's experimental arrangement performed essentially irreversible work, through friction of paddles in a liquid, or passage of electric current through a resistance inside the system, driven by motion of a coil and inductive heating, or by an external current source, which can access the system only by the passage of electrons, and so is not strictly adiabatic, because electrons are a form of matter, which cannot penetrate adiabatic walls. The paper goes on to base its main argument on the possibility of quasi-static adiabatic work, which is essentially reversible. The paper asserts that it will avoid reference to Carnot cycles, and then proceeds to base its argument on cycles of forward and backward quasi-static adiabatic stages, with isothermal stages of zero magnitude. 

Sometimes the concept of internal energy is not made explicit in the statement.

Sometimes the existence of the internal energy is made explicit but work is not explicitly mentioned in the statement of the first postulate of thermodynamics. Heat supplied is then defined as the residual change in internal energy after work has been taken into account, in a non-adiabatic process.

A respected modern author states the first law of thermodynamics as "Heat is a form of energy", which explicitly mentions neither internal energy nor adiabatic work. Heat is defined as energy transferred by thermal contact with a reservoir, which has a temperature, and is generally so large that addition and removal of heat do not alter its temperature. A current student text on chemistry defines heat thus: "heat is the exchange of thermal energy between a system and its surroundings caused by a temperature difference." The author then explains how heat is defined or measured by calorimetry, in terms of heat capacity, specific heat capacity, molar heat capacity, and temperature.

A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined along with work and internal energy. Another respected text defines heat exchange as determined by temperature difference, but also mentions that the Born (1921) version is "completely rigorous". These versions follow the traditional approach that is now considered out of date, exemplified by that of Planck (1897/1903).

Evidence for the first law of thermodynamics for closed systems

The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system. The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes.

The following is an account in terms of changes of state of a closed system through compound processes that are not necessarily cyclic. This account first considers processes for which the first law is easily verified because of their simplicity, namely adiabatic processes (in which there is no transfer as heat) and adynamic processes (in which there is no transfer as work).

Adiabatic processes

In an adiabatic process, there is transfer of energy as work but not as heat. For all adiabatic process that takes a system from a given initial state to a given final state, irrespective of how the work is done, the respective eventual total quantities of energy transferred as work are one and the same, determined just by the given initial and final states. The work done on the system is defined and measured by changes in mechanical or quasi-mechanical variables external to the system. Physically, adiabatic transfer of energy as work requires the existence of adiabatic enclosures.

For instance, in Joule's experiment, the initial system is a tank of water with a paddle wheel inside. If we isolate the tank thermally, and move the paddle wheel with a pulley and a weight, we can relate the increase in temperature with the distance descended by the mass. Next, the system is returned to its initial state, isolated again, and the same amount of work is done on the tank using different devices (an electric motor, a chemical battery, a spring,...). In every case, the amount of work can be measured independently. The return to the initial state is not conducted by doing adiabatic work on the system. The evidence shows that the final state of the water (in particular, its temperature and volume) is the same in every case. It is irrelevant if the work is electrical, mechanical, chemical,... or if done suddenly or slowly, as long as it is performed in an adiabatic way, that is to say, without heat transfer into or out of the system. 

Evidence of this kind shows that to increase the temperature of the water in the tank, the qualitative kind of adiabatically performed work does not matter. No qualitative kind of adiabatic work has ever been observed to decrease the temperature of the water in the tank.

A change from one state to another, for example an increase of both temperature and volume, may be conducted in several stages, for example by externally supplied electrical work on a resistor in the body, and adiabatic expansion allowing the body to do work on the surroundings. It needs to be shown that the time order of the stages, and their relative magnitudes, does not affect the amount of adiabatic work that needs to be done for the change of state. According to one respected scholar: "Unfortunately, it does not seem that experiments of this kind have ever been carried out carefully. ... We must therefore admit that the statement which we have enunciated here, and which is equivalent to the first law of thermodynamics, is not well founded on direct experimental evidence." Another expression of this view is "... no systematic precise experiments to verify this generalization directly have ever been attempted."

This kind of evidence, of independence of sequence of stages, combined with the above-mentioned evidence, of independence of qualitative kind of work, would show the existence of an important state variable that corresponds with adiabatic work, but not that such a state variable represented a conserved quantity. For the latter, another step of evidence is needed, which may be related to the concept of reversibility, as mentioned below.

That important state variable was first recognized and denoted ${\displaystyle U}$ by Clausius in 1850, but he did not then name it, and he defined it in terms not only of work but also of heat transfer in the same process. It was also independently recognized in 1850 by Rankine, who also denoted it ${\displaystyle U}$ ; and in 1851 by Kelvin who then called it "mechanical energy", and later "intrinsic energy". In 1865, after some hestitation, Clausius began calling his state function ${\displaystyle U}$ "energy". In 1882 it was named as the internal energy by Helmholtz. If only adiabatic processes were of interest, and heat could be ignored, the concept of internal energy would hardly arise or be needed. The relevant physics would be largely covered by the concept of potential energy, as was intended in the 1847 paper of Helmholtz on the principle of conservation of energy, though that did not deal with forces that cannot be described by a potential, and thus did not fully justify the principle. Moreover, that paper was critical of the early work of Joule that had by then been performed. A great merit of the internal energy concept is that it frees thermodynamics from a restriction to cyclic processes, and allows a treatment in terms of thermodynamic states.

In an adiabatic process, adiabatic work takes the system either from a reference state ${\displaystyle O}$ with internal energy ${\displaystyle U(O)}$ to an arbitrary one ${\displaystyle A}$ with internal energy ${\displaystyle U(A)}$, or from the state ${\displaystyle A}$ to the state ${\displaystyle O}$:

${\displaystyle U(A)=U(O)-W_{O\to A}^{\mathrm {adiabatic} }\,\,\mathrm {or} \,\,U(O)=U(A)-W_{A\to O}^{\mathrm {adiabatic} }\,.}$

Except under the special, and strictly speaking, fictional, condition of reversibility, only one of the processes  ${\displaystyle \mathrm {adiabatic} ,\,O\to A}$   or  ${\displaystyle \mathrm {adiabatic} ,\,{A\to O}\,}$  is empirically feasible by a simple application of externally supplied work. The reason for this is given as the second law of thermodynamics and is not considered in the present article. 

The fact of such irreversibility may be dealt with in two main ways, according to different points of view:

• Since the work of Bryan (1907), the most accepted way to deal with it nowadays, followed by Carathéodory, is to rely on the previously established concept of quasi-static processes, as follows. Actual physical processes of transfer of energy as work are always at least to some degree irreversible. The irreversibility is often due to mechanisms known as dissipative, that transform bulk kinetic energy into internal energy. Examples are friction and viscosity. If the process is performed more slowly, the frictional or viscous dissipation is less. In the limit of infinitely slow performance, the dissipation tends to zero and then the limiting process, though fictional rather than actual, is notionally reversible, and is called quasi-static. Throughout the course of the fictional limiting quasi-static process, the internal intensive variables of the system are equal to the external intensive variables, those that describe the reactive forces exerted by the surroundings. This can be taken to justify the formula

${\displaystyle (1)\,\,\,\,\,\,\,W_{A\to O}^{\text{adiabatic, quasi-static}}=-W_{O\to A}^{\text{adiabatic, quasi-static}}\,.}$

• Another way to deal with it is to allow that experiments with processes of heat transfer to or from the system may be used to justify the formula (1) above. Moreover, it deals to some extent with the problem of lack of direct experimental evidence that the time order of stages of a process does not matter in the determination of internal energy. This way does not provide theoretical purity in terms of adiabatic work processes, but is empirically feasible, and is in accord with experiments actually done, such as the Joule experiments mentioned just above, and with older traditions.

The formula (1) above allows that to go by processes of quasi-static adiabatic work from the state ${\displaystyle A}$ to the state ${\displaystyle B}$ we can take a path that goes through the reference state ${\displaystyle O}$, since the quasi-static adiabatic work is independent of the path

${\displaystyle -W_{A\to B}^{\mathrm {adiabatic,\,quasi-static} }=-W_{A\to O}^{\mathrm {adiabatic,\,quasi-static} }-W_{O\to B}^{\mathrm {adiabatic,\,quasi-static} }=W_{O\to A}^{\mathrm {adiabatic,\,quasi-static} }-W_{O\to B}^{\mathrm {adiabatic,\,quasi-static} }=-U(A)+U(B)=\Delta U}$

This kind of empirical evidence, coupled with theory of this kind, largely justifies the following statement:

For all adiabatic processes between two specified states of a closed system of any nature, the net work done is the same regardless the details of the process, and determines a state function called internal energy, ${\displaystyle U}$.

Adynamic processes

A complementary observable aspect of the first law is about heat transfer. Adynamic transfer of energy as heat can be measured empirically by changes in the surroundings of the system of interest by calorimetry. This again requires the existence of adiabatic enclosure of the entire process, system and surroundings, though the separating wall between the surroundings and the system is thermally conductive or radiatively permeable, not adiabatic. A calorimeter can rely on measurement of sensible heat, which requires the existence of thermometers and measurement of temperature change in bodies of known sensible heat capacity under specified conditions; or it can rely on the measurement of latent heat, through measurement of masses of material that change phase, at temperatures fixed by the occurrence of phase changes under specified conditions in bodies of known latent heat of phase change. The calorimeter can be calibrated by adiabatically doing externally determined work on it. The most accurate method is by passing an electric current from outside through a resistance inside the calorimeter. The calibration allows comparison of calorimetric measurement of quantity of heat transferred with quantity of energy transferred as work. According to one textbook, "The most common device for measuring ${\displaystyle \Delta U}$ is an adiabatic bomb calorimeter." According to another textbook, "Calorimetry is widely used in present day laboratories." According to one opinion, "Most thermodynamic data come from calorimetry..." According to another opinion, "The most common method of measuring "heat" is with a calorimeter."

When the system evolves with transfer of energy as heat, without energy being transferred as work, in an adynamic process, the heat transferred to the system is equal to the increase in its internal energy:

${\displaystyle Q_{A\to B}^{\mathrm {adynamic} }=\Delta U\,.}$

General case for reversible processes

Heat transfer is practically reversible when it is driven by practically negligibly small temperature gradients. Work transfer is practically reversible when it occurs so slowly that there are no frictional effects within the system; frictional effects outside the system should also be zero if the process is to be globally reversible. For a particular reversible process in general, the work done reversibly on the system, ${\displaystyle W_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }}$, and the heat transferred reversibly to the system, ${\displaystyle Q_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }}$ are not required to occur respectively adiabatically or adynamically, but they must belong to the same particular process defined by its particular reversible path, ${\displaystyle P_{0}}$, through the space of thermodynamic states. Then the work and heat transfers can occur and be calculated simultaneously.

Putting the two complementary aspects together, the first law for a particular reversible process can be written

${\displaystyle -W_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }+Q_{A\to B}^{\mathrm {path} \,P_{0},\,\mathrm {reversible} }=\Delta U\,.}$

This combined statement is the expression the first law of thermodynamics for reversible processes for closed systems. 

In particular, if no work is done on a thermally isolated closed system we have

${\displaystyle \Delta U=0\,}$.

This is one aspect of the law of conservation of energy and can be stated:

The internal energy of an isolated system remains constant.

General case for irreversible processes

If, in a process of change of state of a closed system, the energy transfer is not under a practically zero temperature gradient and practically frictionless, then the process is irreversible. Then the heat and work transfers may be difficult to calculate, and irreversible thermodynamics is called for. Nevertheless, the first law still holds and provides a check on the measurements and calculations of the work done irreversibly on the system, ${\displaystyle W_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }}$, and the heat transferred irreversibly to the system, ${\displaystyle Q_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }}$, which belong to the same particular process defined by its particular irreversible path, ${\displaystyle P_{1}}$, through the space of thermodynamic states:

${\displaystyle -W_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }+Q_{A\to B}^{\mathrm {path} \,P_{1},\,\mathrm {irreversible} }=\Delta U\,.}$

 This means that the internal energy ${\displaystyle U}$ is a function of state and that the internal energy change ${\displaystyle \Delta U}$ between two states is a function only of the two states.

Overview of the weight of evidence for the law

The first law of thermodynamics is so general that its predictions cannot all be directly tested. In many properly conducted experiments it has been precisely supported, and never violated. Indeed, within its scope of applicability, the law is so reliably established, that, nowadays, rather than experiment being considered as testing the accuracy of the law, it is more practical and realistic to think of the law as testing the accuracy of experiment. An experimental result that seems to violate the law may be assumed to be inaccurate or wrongly conceived, for example due to failure to account for an important physical factor. Thus, some may regard it as a principle more abstract than a law.

State functional formulation for infinitesimal processes

When the heat and work transfers in the equations above are infinitesimal in magnitude, they are often denoted by δ, rather than exact differentials denoted by d, as a reminder that heat and work do not describe the state of any system. The integral of an inexact differential depends upon the particular path taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the integral of an exact differential is always zero. The path taken by a thermodynamic system through a chemical or physical change is known as a thermodynamic process. 

The first law for a closed homogeneous system may be stated in terms that include concepts that are established in the second law. The internal energy U may then be expressed as a function of the system's defining state variables S, entropy, and V, volume: U = U (S, V). In these terms, T, the system's temperature, and P, its pressure, are partial derivatives of U with respect to S and V. These variables are important throughout thermodynamics, though not necessary for the statement of the first law. Rigorously, they are defined only when the system is in its own state of internal thermodynamic equilibrium. For some purposes, the concepts provide good approximations for scenarios sufficiently near to the system's internal thermodynamic equilibrium.

The first law requires that:

${\displaystyle dU=\delta Q-\delta W\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, general process, quasi-static or irreversible).}}}$

Then, for the fictive case of a reversible process, dU can be written in terms of exact differentials. One may imagine reversible changes, such that there is at each instant negligible departure from thermodynamic equilibrium within the system. This excludes isochoric work. Then, mechanical work is given by δW = - P dV and the quantity of heat added can be expressed as δQ = T dS. For these conditions

${\displaystyle dU=TdS-PdV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, reversible process).}}}$

While this has been shown here for reversible changes, it is valid in general, as U can be considered as a thermodynamic state function of the defining state variables S and V:

${\displaystyle (2)\,\,\,\,\,\,\,dU=TdS-PdV\,\,\,\,\,{\text{(closed system, general process, quasi-static or irreversible).}}}$

Equation (2) is known as the fundamental thermodynamic relation for a closed system in the energy representation, for which the defining state variables are S and V, with respect to which T and P are partial derivatives of U. It is only in the fictive reversible case, when isochoric work is excluded, that the work done and heat transferred are given by −P dV and T dS.

In the case of a closed system in which the particles of the system are of different types and, because chemical reactions may occur, their respective numbers are not necessarily constant, the fundamental thermodynamic relation for dU becomes:

${\displaystyle dU=TdS-PdV+\sum _{i}\mu _{i}dN_{i}.\,}$

where dN_i is the (small) increase in amount of type-i particles in the reaction, and μ_i is known as the chemical potential of the type-i particles in the system. If dN_i is expressed in mol then μ_i is expressed in J/mol. If the system has more external mechanical variables than just the volume that can change, the fundamental thermodynamic relation further generalizes to:

${\displaystyle dU=TdS-\sum _{i}X_{i}dx_{i}+\sum _{j}\mu _{j}dN_{j}.\,}$

Here the X_i are the generalized forces corresponding to the external variables x_i. The parameters X_i are independent of the size of the system and are called intensive parameters and the x_i are proportional to the size and called extensive parameters. 

For an open system, there can be transfers of particles as well as energy into or out of the system during a process. For this case, the first law of thermodynamics still holds, in the form that the internal energy is a function of state and the change of internal energy in a process is a function only of its initial and final states, as noted in the section below headed First law of thermodynamics for open systems. 

A useful idea from mechanics is that the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating term: dU = -PdV. The pressure P can be viewed as a force (and in fact has units of force per unit area) while dVis the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two (work) is the amount of energy transferred out of the system as a result of the process. If one were to make this term negative then this would be the work done on the system.

It is useful to view the TdS term in the same light: here the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

Similarly, a difference in chemical potential between groups of particles in the system drives a chemical reaction that changes the numbers of particles, and the corresponding product is the amount of chemical potential energy transformed in process. For example, consider a system consisting of two phases: liquid water and water vapor. There is a generalized "force" of evaporation that drives water molecules out of the liquid. There is a generalized "force" of condensation that drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal is there equilibrium, and the net rate of transfer zero.

The two thermodynamic parameters that form a generalized force-displacement pair are called "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

Spatially inhomogeneous systems

Classical thermodynamics is initially focused on closed homogeneous systems (e.g. Planck 1897/1903), which might be regarded as 'zero-dimensional' in the sense that they have no spatial variation. But it is desired to study also systems with distinct internal motion and spatial inhomogeneity. For such systems, the principle of conservation of energy is expressed in terms not only of internal energy as defined for homogeneous systems, but also in terms of kinetic energy and potential energies of parts of the inhomogeneous system with respect to each other and with respect to long-range external forces. How the total energy of a system is allocated between these three more specific kinds of energy varies according to the purposes of different writers; this is because these components of energy are to some extent mathematical artifacts rather than actually measured physical quantities. For any closed homogeneous component of an inhomogeneous closed system, if ${\displaystyle E}$ denotes the total energy of that component system, one may write

${\displaystyle E=E^{\mathrm {kin} }+E^{\mathrm {pot} }+U}$,

where ${\displaystyle E^{\mathrm {kin} }}$ and ${\displaystyle E^{\mathrm {pot} }}$ denote respectively the total kinetic energy and the total potential energy of the component closed homogeneous system, and ${\displaystyle U}$ denotes its internal energy.

Potential energy can be exchanged with the surroundings of the system when the surroundings impose a force field, such as gravitational or electromagnetic, on the system.

A compound system consisting of two interacting closed homogeneous component subsystems has a potential energy of interaction ${\displaystyle E_{12}^{\mathrm {pot} }}$ between the subsystems. Thus, in an obvious notation, one may write

${\displaystyle E=E_{1}^{\mathrm {kin} }+E_{1}^{\mathrm {pot} }+U_{1}+E_{2}^{\mathrm {kin} }+E_{2}^{\mathrm {pot} }+U_{2}+E_{12}^{\mathrm {pot} }}$.

The quantity ${\displaystyle E_{12}^{\mathrm {pot} }}$ in general lacks an assignment to either subsystem in a way that is not arbitrary, and this stands in the way of a general non-arbitrary definition of transfer of energy as work. On occasions, authors make their various respective arbitrary assignments.

The distinction between internal and kinetic energy is hard to make in the presence of turbulent motion within the system, as friction gradually dissipates macroscopic kinetic energy of localised bulk flow into molecular random motion of molecules that is classified as internal energy. The rate of dissipation by friction of kinetic energy of localised bulk flow into internal energy, whether in turbulent or in streamlined flow, is an important quantity in non-equilibrium thermodynamics. This is a serious difficulty for attempts to define entropy for time-varying spatially inhomogeneous systems.

First law of thermodynamics for open systems

For the first law of thermodynamics, there is no trivial passage of physical conception from the closed system view to an open system view. For closed systems, the concepts of an adiabatic enclosure and of an adiabatic wall are fundamental. Matter and internal energy cannot permeate or penetrate such a wall. For an open system, there is a wall that allows penetration by matter. In general, matter in diffusive motion carries with it some internal energy, and some microscopic potential energy changes accompany the motion. An open system is not adiabatically enclosed.

There are some cases in which a process for an open system can, for particular purposes, be considered as if it were for a closed system. In an open system, by definition hypothetically or potentially, matter can pass between the system and its surroundings. But when, in a particular case, the process of interest involves only hypothetical or potential but no actual passage of matter, the process can be considered as if it were for a closed system.

Internal energy for an open system

Since the revised and more rigorous definition of the internal energy of a closed system rests upon the possibility of processes by which adiabatic work takes the system from one state to another, this leaves a problem for the definition of internal energy for an open system, for which adiabatic work is not in general possible. According to Max Born, the transfer of matter and energy across an open connection "cannot be reduced to mechanics". In contrast to the case of closed systems, for open systems, in the presence of diffusion, there is no unconstrained and unconditional physical distinction between convective transfer of internal energy by bulk flow of matter, the transfer of internal energy without transfer of matter (usually called heat conduction and work transfer), and change of various potential energies. The older traditional way and the conceptually revised (Carathéodory) way agree that there is no physically unique definition of heat and work transfer processes between open systems.

In particular, between two otherwise isolated open systems an adiabatic wall is by definition impossible. This problem is solved by recourse to the principle of conservation of energy. This principle allows a composite isolated system to be derived from two other component non-interacting isolated systems, in such a way that the total energy of the composite isolated system is equal to the sum of the total energies of the two component isolated systems. Two previously isolated systems can be subjected to the thermodynamic operation of placement between them of a wall permeable to matter and energy, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new single unpartitioned system. The internal energies of the initial two systems and of the final new system, considered respectively as closed systems as above, can be measured. Then the law of conservation of energy requires that

${\displaystyle \Delta U_{s}+\Delta U_{o}=0\,,}$

$$

where ΔU_s and ΔU_o denote the changes in internal energy of the system and of its surroundings respectively. This is a statement of the first law of thermodynamics for a transfer between two otherwise isolated open systems, that fits well with the conceptually revised and rigorous statement of the law stated above. 

For the thermodynamic operation of adding two systems with internal energies U₁ and U₂, to produce a new system with internal energy U, one may write U = U₁ + U₂; the reference states for U, U₁ and U₂ should be specified accordingly, maintaining also that the internal energy of a system be proportional to its mass, so that the internal energies are extensive variables.

There is a sense in which this kind of additivity expresses a fundamental postulate that goes beyond the simplest ideas of classical closed system thermodynamics; the extensivity of some variables is not obvious, and needs explicit expression; indeed one author goes so far as to say that it could be recognized as a fourth law of thermodynamics, though this is not repeated by other authors.

Also, of course

${\displaystyle \Delta N_{s}+\Delta N_{o}=0\,,}$

where ΔN_s and ΔN_o denote the changes in mole number of a component substance of the system and of its surroundings respectively. This is a statement of the law of conservation of mass.

Process of transfer of matter between an open system and its surroundings

A system connected to its surroundings only through contact by a single permeable wall, but otherwise isolated, is an open system. If it is initially in a state of contact equilibrium with a surrounding subsystem, a thermodynamic process of transfer of matter can be made to occur between them if the surrounding subsystem is subjected to some thermodynamic operation, for example, removal of a partition between it and some further surrounding subsystem. The removal of the partition in the surroundings initiates a process of exchange between the system and its contiguous surrounding subsystem. 

An example is evaporation. One may consider an open system consisting of a collection of liquid, enclosed except where it is allowed to evaporate into or to receive condensate from its vapor above it, which may be considered as its contiguous surrounding subsystem, and subject to control of its volume and temperature. 

A thermodynamic process might be initiated by a thermodynamic operation in the surroundings, that mechanically increases in the controlled volume of the vapor. Some mechanical work will be done within the surroundings by the vapor, but also some of the parent liquid will evaporate and enter the vapor collection which is the contiguous surrounding subsystem. Some internal energy will accompany the vapor that leaves the system, but it will not make sense to try to uniquely identify part of that internal energy as heat and part of it as work. Consequently, the energy transfer that accompanies the transfer of matter between the system and its surrounding subsystem cannot be uniquely split into heat and work transfers to or from the open system. The component of total energy transfer that accompanies the transfer of vapor into the surrounding subsystem is customarily called 'latent heat of evaporation', but this use of the word heat is a quirk of customary historical language, not in strict compliance with the thermodynamic definition of transfer of energy as heat. In this example, kinetic energy of bulk flow and potential energy with respect to long-range external forces such as gravity are both considered to be zero. The first law of thermodynamics refers to the change of internal energy of the open system, between its initial and final states of internal equilibrium.

Open system with multiple contacts

An open system can be in contact equilibrium with several other systems at once.

This includes cases in which there is contact equilibrium between the system, and several subsystems in its surroundings, including separate connections with subsystems through walls that are permeable to the transfer of matter and internal energy as heat and allowing friction of passage of the transferred matter, but immovable, and separate connections through adiabatic walls with others, and separate connections through diathermic walls impermeable to matter with yet others. Because there are physically separate connections that are permeable to energy but impermeable to matter, between the system and its surroundings, energy transfers between them can occur with definite heat and work characters. Conceptually essential here is that the internal energy transferred with the transfer of matter is measured by a variable that is mathematically independent of the variables that measure heat and work.

With such independence of variables, the total increase of internal energy in the process is then determined as the sum of the internal energy transferred from the surroundings with the transfer of matter through the walls that are permeable to it, and of the internal energy transferred to the system as heat through the diathermic walls, and of the energy transferred to the system as work through the adiabatic walls, including the energy transferred to the system by long-range forces. These simultaneously transferred quantities of energy are defined by events in the surroundings of the system. Because the internal energy transferred with matter is not in general uniquely resolvable into heat and work components, the total energy transfer cannot in general be uniquely resolved into heat and work components. Under these conditions, the following formula can describe the process in terms of externally defined thermodynamic variables, as a statement of the first law of thermodynamics:

${\displaystyle (3)\,\,\,\,\,\,\,\Delta U_{0}\,=\,Q\,-\,W\,-\,\sum _{i=1}^{m}\Delta U_{i}\,\,\,\,\,{\text{(suitably defined surrounding subsystems, general process, quasi-static or irreversible),}}}$

where ΔU₀ denotes the change of internal energy of the system, and ΔU_i denotes the change of internal energy of the ith of the m surrounding subsystems that are in open contact with the system, due to transfer between the system and that ith surrounding subsystem, and Q denotes the internal energy transferred as heat from the heat reservoir of the surroundings to the system, and W denotes the energy transferred from the system to the surrounding subsystems that are in adiabatic connection with it. The case of a wall that is permeable to matter and can move so as to allow transfer of energy as work is not considered here.

Combination of first and second laws

If the system is described by the energetic fundamental equation, U₀ = U₀(S, V, N_j), and if the process can be described in the quasi-static formalism, in terms of the internal state variables of the system, then the process can also be described by a combination of the first and second laws of thermodynamics, by the formula

${\displaystyle (4)\,\,\,\,\,\,\,\mathrm {d} U_{0}\,=\,T\,\mathrm {d} S\,-\,P\,\mathrm {d} V\,+\,\sum _{j=1}^{n}\mu _{j}\,\mathrm {d} N_{j}}$

where there are n chemical constituents of the system and permeably connected surrounding subsystems, and where T, S, P, V, N_j, and μ_j, are defined as above.

For a general natural process, there is no immediate term-wise correspondence between equations (3) and (4), because they describe the process in different conceptual frames. 

Nevertheless, a conditional correspondence exists. There are three relevant kinds of wall here: purely diathermal, adiabatic, and permeable to matter. If two of those kinds of wall are sealed off, leaving only one that permits transfers of energy, as work, as heat, or with matter, then the remaining permitted terms correspond precisely. If two of the kinds of wall are left unsealed, then energy transfer can be shared between them, so that the two remaining permitted terms do not correspond precisely. 

For the special fictive case of quasi-static transfers, there is a simple correspondence. For this, it is supposed that the system has multiple areas of contact with its surroundings. There are pistons that allow adiabatic work, purely diathermal walls, and open connections with surrounding subsystems of completely controllable chemical potential (or equivalent controls for charged species). Then, for a suitable fictive quasi-static transfer, one can write

${\displaystyle \delta Q\,=\,T\,\mathrm {d} S\,{\text{ and }}\delta W\,=\,P\,\mathrm {d} V\,\,\,\,\,\,{\text{(suitably defined surrounding subsystems, quasi-static transfers of energy)}}.}$

For fictive quasi-static transfers for which the chemical potentials in the connected surrounding subsystems are suitably controlled, these can be put into equation (4) to yield

${\displaystyle (5)\,\,\,\,\,\,\,\mathrm {d} U_{0}\,=\,\delta Q\,-\,\delta W\,+\,\sum _{j=1}^{n}\mu _{j}\,\mathrm {d} N_{j}\,\,\,\,\,\,\,{\text{(suitably defined surrounding subsystems, quasi-static transfers)}}.}$

The reference  does not actually write equation (5), but what it does write is fully compatible with it. Another helpful account is given by Tschoegl.

There are several other accounts of this, in apparent mutual conflict.

Non-equilibrium transfers

The transfer of energy between an open system and a single contiguous subsystem of its surroundings is considered also in non-equilibrium thermodynamics. The problem of definition arises also in this case. It may be allowed that the wall between the system and the subsystem is not only permeable to matter and to internal energy, but also may be movable so as to allow work to be done when the two systems have different pressures. In this case, the transfer of energy as heat is not defined. 

Methods for study of non-equilibrium processes mostly deal with spatially continuous flow systems. In this case, the open connection between system and surroundings is usually taken to fully surround the system, so that there are no separate connections impermeable to matter but permeable to heat. Except for the special case mentioned above when there is no actual transfer of matter, which can be treated as if for a closed system, in strictly defined thermodynamic terms, it follows that transfer of energy as heat is not defined. In this sense, there is no such thing as 'heat flow' for a continuous-flow open system. Properly, for closed systems, one speaks of transfer of internal energy as heat, but in general, for open systems, one can speak safely only of transfer of internal energy. A factor here is that there are often cross-effects between distinct transfers, for example that transfer of one substance may cause transfer of another even when the latter has zero chemical potential gradient. 

Usually transfer between a system and its surroundings applies to transfer of a state variable, and obeys a balance law, that the amount lost by the donor system is equal to the amount gained by the receptor system. Heat is not a state variable. For his 1947 definition of "heat transfer" for discrete open systems, the author Prigogine carefully explains at some length that his definition of it does not obey a balance law. He describes this as paradoxical.

The situation is clarified by Gyarmati, who shows that his definition of "heat transfer", for continuous-flow systems, really refers not specifically to heat, but rather to transfer of internal energy, as follows. He considers a conceptual small cell in a situation of continuous-flow as a system defined in the so-called Lagrangian way, moving with the local center of mass. The flow of matter across the boundary is zero when considered as a flow of total mass. Nevertheless, if the material constitution is of several chemically distinct components that can diffuse with respect to one another, the system is considered to be open, the diffusive flows of the components being defined with respect to the center of mass of the system, and balancing one another as to mass transfer. Still there can be a distinction between bulk flow of internal energy and diffusive flow of internal energy in this case, because the internal energy density does not have to be constant per unit mass of material, and allowing for non-conservation of internal energy because of local conversion of kinetic energy of bulk flow to internal energy by viscosity. 

Gyarmati shows that his definition of "the heat flow vector" is strictly speaking a definition of flow of internal energy, not specifically of heat, and so it turns out that his use here of the word heat is contrary to the strict thermodynamic definition of heat, though it is more or less compatible with historical custom, that often enough did not clearly distinguish between heat and internal energy; he writes "that this relation must be considered to be the exact definition of the concept of heat flow, fairly loosely used in experimental physics and heat technics." Apparently in a different frame of thinking from that of the above-mentioned paradoxical usage in the earlier sections of the historic 1947 work by Prigogine, about discrete systems, this usage of Gyarmati is consistent with the later sections of the same 1947 work by Prigogine, about continuous-flow systems, which use the term "heat flux" in just this way. This usage is also followed by Glansdorff and Prigogine in their 1971 text about continuous-flow systems. They write: "Again the flow of internal energy may be split into a convection flow ρuv and a conduction flow. This conduction flow is by definition the heat flow W. Therefore: j[U] = ρuv + W where u denotes the [internal] energy per unit mass. [These authors actually use the symbols E and e to denote internal energy but their notation has been changed here to accord with the notation of the present article. These authors actually use the symbol U to refer to total energy, including kinetic energy of bulk flow.]" This usage is followed also by other writers on non-equilibrium thermodynamics such as Lebon, Jou, and Casas-Vásquez, and de Groot and Mazur. This usage is described by Bailyn as stating the non-convective flow of internal energy, and is listed as his definition number 1, according to the first law of thermodynamics. This usage is also followed by workers in the kinetic theory of gases. This is not the ad hoc definition of "reduced heat flux" of Haase.

In the case of a flowing system of only one chemical constituent, in the Lagrangian representation, there is no distinction between bulk flow and diffusion of matter. Moreover, the flow of matter is zero into or out of the cell that moves with the local center of mass. In effect, in this description, one is dealing with a system effectively closed to the transfer of matter. But still one can validly talk of a distinction between bulk flow and diffusive flow of internal energy, the latter driven by a temperature gradient within the flowing material, and being defined with respect to the local center of mass of the bulk flow. In this case of a virtually closed system, because of the zero matter transfer, as noted above, one can safely distinguish between transfer of energy as work, and transfer of internal energy as heat.