First law of Thermodynamics

"The total work is the same in all adiabatic processes between any two equilibrium states having the same
kinetic and potential energies". We generalize this to include the internal energy. This is just
conservation of energy:

The First Law of thermodynamics is simply the law of conservation of energy and mass. The ready acceptability of this law is apparent from the fact that the concept of conservation in some form has existed from antiquity, long before any precise demonstration of it could be made. The ancient biblical affirmation, "What so ever a man sows, that shall he also reap" is, in a sense, a conservation law. The Greek philosophers generally considered matter to be indestructible, although its forms--earth, fire, air, or water-- could be interchanged. The situation was confused in the Middle Ages by a feeling that a combustion process actually "destroyed" the matter which burned. This was not set right until 1774 when Lavoisier conclusively demonstrated the conservation of mass in chemical
reactions.

It is fortunate that an intuitive feeling for energy conservation is also deep-rooted because its demonstration is experimentally more difficult than that for mass conservation and that which is conserved is more abstract.

From an intuitive sense of universal justice, we feel that this quantity should be universally conserved, never created from nothing, never destroyed without a trace, but transformable into other forms with the total quantity before and after the transformation remaining the same.
The earliest demonstration of energy conservation is generally credited to Count Rumford in 1797. Fortunately, he made his observations in a cannon factory where the mechanical work of boring a cannon was converted into heat and transferred to a large amount of cooling water. If this heat transfer had not been very large relative to the heat
losses, the correct conclusion could easily have escaped him. The first accurate measurement and indisputable demonstration of the precise equivalence of mechanical work and the total thermal energy obtainable from it did not occur until the experiments of Joule and Kelvin between 1843 and 1848 were done.

At present, when mass and energy can be shown to be mutually interchangeable, conservation of mass and conservation of energy should be combined into a single conservation law which, as far as we know, is universal. At the magnitude of energies involved in thermodynamic state changes the accompanying mass changes are negligible so that mass and energy are always considered to be conserved separately.

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