All the relations connecting the internal energy, entropy, and temperature of thermodynamic systems with other macroscopic quantities (such as isothermal compressibility, thermal expansivity, heat capacity, etc.) can be derived on the basis of this theory. But the actual values of thermodynamic quantities are not given by thermodynamic theory; they must be measured in the laboratory, or calculated by statistical mechanics.
It can be shown from the first and second parts of the second law that the most efficient cycle for a heat engine converting heat into work is the Carnot cycle.
The proof is based on the fact that the system, after increasing its entropy by absorbing heat at a high absolute temperature, must reject some heat at a low absolute temperature to return to its initial entropy. The greatest amount of mechanical work is obtained when the heat rejected is the least. This means that (a) the heat should be absorbed without any temperature difference between the source and the working thermodynamic system, (b) the rejection of heat should be at the lowest possible temperature, and (c) the entropy produced by irreversibilities should be zero.
The Kelvin-Planck and Clausius statements of the second law of thermodynamics are corollaries of this result.
By R. H. B. Exell, 2001. King Mongkut's University of Technology Thonburi.
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