THERMODYNAMICS

The Zeroth Law of Thermodynamics

The zeroth law may be stated as follows:

Two thermodynamic systems in thermal equilibrium with the same environment are in thermal equilibrium with each other.

The zeroth law does not appear as a basic postulate in this new theory for the following two reasons:

1. There exist experimental situations where the zeroth law fails. For example, a system which emits neutrons, and another system which absorbs neutrons may separately be in thermal equilibrium with the environment; but they will not be in thermal equilibrium with each other because of the neutron interactions. Therefore the zeroth law can be viewed as a definition of thermal interactions, which is already included in the theory of diathermal walls.
2. The zeroth law is a consequence of the first and second laws of thermodynamics. This is proved as follows: Let systems A and B be in thermal equilibrium with the environment, and suppose that B is hotter than A, violating the zeroth law. Expand B reversibly until it is in thermal equilibrium with A. Then put A and B in thermal contact, and compress B reversibly to its original volume. Since B loses heat to A during the compression, the work of compression of B is less than the work of expansion, and there is a net output of work. Finally, let A and B be returned separately by thermal contact to equilibrium with the environment. The overall result is a complete conversion of heat from the environment into work in a cyclic process violating Kelvin's statement of the second law.

By R. H. B. Exell, 2001. King Mongkut's University of Technology Thonburi.
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