Conservation of energy and the mechanical equivalent of heat

Helmholtz set out the principle in his 1847 work Über die Erhaltung der Kraft. In it he applied the principle to galvanic currents. He divided them into currents that produce polarisation and currents that produce decomposition, a division he said the principle conditions¹. He believed this might be the only way to avoid the difficulties of both the chemical theory and the contact theory¹. For thermoelectric currents he looked for the source of the force in the effects Peltier had found at the soldered junctions¹.

Timiriazeff (1912), in The Life of the Plant, stated that when mechanical work turns into heat, or heat into work, a constant and strictly quantitative ratio is observed⁴. The number that expresses it is the mechanical equivalent of heat⁴. He described Hirn's method, in which an iron hammer falls from a known height onto lead lying on an anvil and the lead grows hot. He called it simple and obvious but not very accurate⁴. He quoted Faraday, who called the law the highest in physical science that our faculties permit us to perceive⁵. He also noted cases where the law seems not to hold, as with balls that knock together⁵.

Verworn (1899), in General Physiology, argued that the chemical energy taken in with food, expressed in calories, must equal the heat the body gives off. He reported that the experiments reached this result with all desired exactness, so the law was confirmed for the living body². Driesch (1908) wrote that conservation means a quantity is retained through causal processes while its character changes³. Crile (1926) listed among his propositions that the living transformer of energy obeys the same laws as non-living ones⁶. Hill (1926) granted that thermodynamics gives only a partial picture, but said the certainty of applying the principle gives firm ground⁷.

Thompson, in On Growth and Form, cites Helmholtz's 1861 lecture on the conservation of forces applied to organic nature. Helmholtz held that forces in the living body, as far as they cause chemical and mechanical effects, must be of the same character as inorganic forces and ruled by necessity⁸. Thompson drew the conclusion that such forces are open to mathematical analysis⁸. Fields, Glazebrook and Levin (2021) carry the principle into cognition. Their minimal physicalism treats information and energy as formally equivalent, enforces conservation of energy, and so requires the thermodynamics of classical computation⁹. They add that it enforces a metabolism and cognition tradeoff⁹.