
The first law of thermodynamics, a formulation of the law of conservation of energy in the context of thermodynamic processes, is believed to have been developed almost simultaneously by Julius Robert Mayer and James Prescot Joule in the 1840s. However, the first explicit statement of the first law of thermodynamics was made by Rudolf Clausius in 1850, referring to cyclic thermodynamic processes and the existence of a function of state of the system, the internal energy.
| Characteristics | Values |
|---|---|
| Year of Discovery | 1840s |
| Discoverers | Julius Robert Mayer, James Prescot Joule, Rudolf Clausius, William Thomson |
| Basis of the First Law | Quantitative measurements to compare the amount of mechanical work and heat that would raise the temperature of a known quantity of water by the same amount |
| Definition | A formulation of the law of conservation of energy in the context of thermodynamic processes |
| Other Names | Hess's Law, Mayer-Joule Principle |
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What You'll Learn

The work of Rudolf Clausius
Rudolf Clausius (1822-1888) is considered one of the central founders of the science of thermodynamics. In 1850, Clausius published his most famous paper, "On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom", which dealt with the mechanical theory of heat. In this paper, he showed there was a contradiction between Carnot's principle and the concept of conservation of energy. Clausius restated the two laws of thermodynamics to overcome this contradiction. This paper made him famous among scientists.
In 1849, Clausius read a paper about the theories of heat by Sadi Carnot, a long-deceased French scientist. Recognizing the significance of James Prescott Joule's work on the conservation of energy, Clausius was the first to formulate the second law in 1850, in this form: heat does not flow spontaneously from cold to hot bodies. In 1850, Clausius referred to cyclic thermodynamic processes and the existence of a function of state of the system, the internal energy. Although Clausius didn't use the word "energy" for another 13 years, an equation that he created is still used to describe the first law with the same letters and sign conventions today.
In 1865, Clausius introduced the concept of entropy and gave it its name. He defined equivalence-value as entropy, which is now signified by the letter "S" because of him. The most famous version of the second law was read in a presentation at the Philosophical Society of Zurich in 1865, in which Clausius concluded: "The entropy of the universe tends to a maximum." This statement is the best-known phrasing of the second law.
Clausius also contributed to the field of kinetic theory after refining August Krönig's simple gas-kinetic model to include translational, rotational, and vibrational molecular motions.
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The work of James Prescott Joule
James Prescott Joule was an English physicist and mathematician born in 1818 in Salford, England. He is known for formulating Joule's Law, which states that the heat per second evolved by an electrical current passing through a wire is proportional to the current squared and the resistance of the wire. This discovery laid the groundwork for the first law of thermodynamics, also known as the law of conservation of energy.
Joule's interest in the field of thermodynamics began around 1840 when he started investigating the feasibility of replacing the brewery's steam engines with newly invented electric motors. His early scientific papers on the subject were contributed to William Sturgeon's "Annals of Electricity". In 1841, he discovered Joule's First Law, which states that the heat generated by a proper current is proportional to the square of the intensity of that current, multiplied by the resistance to conduction. This discovery challenged the prevalent caloric theory, which stated that heat could neither be created nor destroyed.
Joule's most famous experiments dealt with the conversion of heat energy into mechanical energy and vice versa. He conducted experiments to measure the amount of work an electric motor must do to raise the temperature of a volume of water by one degree. He pumped water through a perforated cylinder and measured the temperature increase in the water. He also measured the heat generated when compressing a gas. In all cases, he found that the amount of mechanical energy applied to the fluid equaled the exact amount of heat energy generated.
In 1843, Joule published the results of his experiments, showing that the heating effect he had quantified in 1841 was due to the generation of heat in the conductor rather than its transfer from another part of the equipment. This provided compelling evidence for the convertibility of work into heat. Joule's work with William Thomson established the Joule-Thomson effect, which states that freely expanding gas cools in temperature. He also worked with Lord Kelvin to create the absolute temperature scale, now known as the Kelvin scale.
The Standard International Unit for energy is now called the "joule" in honour of James Prescott Joule and his significant contributions to the field of thermodynamics.
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The work of Julius Robert Mayer
In 1841, Mayer returned to Heilbronn and began investigating the physical laws governing heat. He performed experiments and wrote a paper on the conservation of heat, which was rejected by the editor of the Annalen der Physik journal. Undeterred, Mayer revised and resubmitted his work to another journal, the Annalen der Chemie und Pharmacie, which published it in 1842. Under the title "Remarks on the Forces of Inorganic Nature" or "Remarks on the Forces of Inanimate Nature." In this publication, Mayer introduced the concept of the mechanical equivalent of heat, calculating that a weight falling from a height of 365 meters to the ground would generate a certain amount of heat. This implied that work and heat are different forms of energy that can be transformed into one another, a fundamental principle in the law of conservation of energy.
Mayer's work in the 1840s, particularly his 1842 publication, is recognized as one of the original statements of the conservation of energy, which became known as the first law of thermodynamics. He is credited with enunciating the principle that "energy can be neither created nor destroyed," only transformed from one form to another. This idea was further supported by his description of oxidation as the primary source of energy for living creatures and his proposal that plants convert light into chemical energy.
Despite the significance of his contributions, Mayer's achievements were initially overlooked, and credit for the discovery of the mechanical equivalent of heat was given to James Joule in 1843. Mayer suffered greatly from this, even contemplating suicide. However, his work gradually gained recognition, and in 1862, physicist John Tyndall delivered a lecture at the London Royal Institution that helped revive interest in Mayer's ideas. Mayer received several honors later in his life, including an honorary doctorate from the University of Tübingen in 1859, the Copley Medal from the Royal Society of London in 1871, and nobility by the Kingdom of Württemberg in 1867.
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The work of Hermann von Helmholtz
Hermann von Helmholtz (1821–1894) was a German physicist and physician who made significant contributions across several scientific fields, including hydrodynamic stability, physiology, psychology, and physics. In the latter, he is known for his theories on the conservation of energy, the electrical double layer, electrodynamics, chemical thermodynamics, and a mechanical foundation of thermodynamics.
Helmholtz is credited with the first formulation of the energy conservation principle in its maximally general form. He participated in two of the most significant developments in physics and the philosophy of science in the 19th century: the proof that Euclidean geometry does not describe the only possible visualizable and physical space, and the shift from physics based on actions between particles at a distance to the field theory.
Helmholtz's work in the physiology and mechanics of perception occasioned much of what he is known for in the philosophy of science, including ideas on the relation between the laws of perception and the laws of nature, and his rejection of the exclusive use of Euclidean geometry. His philosophy of science wavered between some version of empiricism and transcendentalism. Despite the speculative associations of the latter, his philosophy of science is thoroughly indebted to his use of mathematical physics to supplant vitalism and articulate the general conservation of energy principle.
Helmholtz introduced a new conception of the a priori in space: that of the determination of the manifold of possible orientations in perceptual space. This development of a broadly Kantian methodology, including the a priori determination of the manifold of possible orientations in perceptual space, inspired new readings of Kant and contributed to the late modern neo-Kantianism movement in philosophy.
Helmholtz also contributed to the experimental basis of electrodynamics, publishing three parts of "On the Theory of Electrodynamics," in which he responded to Wilhelm Weber and supported Maxwell's assertion that light is an electromagnetic wave in the ether. The debate between Helmholtz and Weber continued until the end of the 1880s, when the explanation of electromagnetic force in terms of action at a distance between particles in the ether gave way to the field theory.
Helmholtz's work in thermodynamics includes the development of the concept of free energy, first presented in 1882 in a lecture called "On the Thermodynamics of Chemical Processes." The Helmholtz free energy is the Legendre transformation of the internal energy U, in which temperature replaces entropy as the independent variable.
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The work of William Thomson
Thomson's work on the first law of thermodynamics was influenced by his interest in heat conduction and the cooling of the Earth. He believed that the laws of thermodynamics had operated since the birth of the universe and envisioned a dynamic process that led to the formation of the Solar System and other structures, followed by a gradual "heat death." This idea of universal heat death, which extended Carnot's theory, was a significant contribution to the development of the second law of thermodynamics. Thomson also formulated the heat death paradox (Kelvin's paradox) in 1862, using the second law of thermodynamics to disprove the possibility of an infinitely old universe.
Thomson's career as an electrical telegraph engineer and inventor brought him public recognition and honours. He was knighted by Queen Victoria in 1866 for his contributions to the transatlantic telegraph project and became Sir William Thomson. His maritime interests led him to work on improving the mariner's compass, which previously had limited reliability. In recognition of his achievements in thermodynamics and his opposition to Irish Home Rule, Thomson was ennobled in 1892, becoming Baron Kelvin.
Thomson's work on the first law of thermodynamics was part of his broader contributions to unifying physics, which was then in its early stages of development as an academic discipline. He received the Royal Society's Copley Medal in 1883 and served as its president from 1890 to 1895. In 1892, he became the first scientist to be elevated to the House of Lords, further honouring his achievements. Thomson's work on the first law of thermodynamics, alongside that of German physicist Rudolf Clausius and others, helped establish the fundamental principles of this field and paved the way for further developments in the understanding of energy and heat transfer.
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Frequently asked questions
The first law of thermodynamics is believed to have been developed almost simultaneously by Julius Robert Mayer and James Prescot Joule in the 1840s. However, the first explicit statement of the law was made by Rudolf Clausius in 1850.
The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. It distinguishes two principal forms of energy transfer, heat and thermodynamic work, and defines the internal energy of a system.
One example of the first law of thermodynamics in action is the functioning of a steam engine. Additionally, in the early 19th century, James Joule performed quantitative measurements to compare the amount of mechanical work and heat required to raise the temperature of a known quantity of water by the same amount.

























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