Second Law of Thermodynamics

The second law of thermodynamics was actually postulated by Carnot prior to the development of the first law. The original statements made concerning the second law were negative—they said what would not happen. The second law states that heat will not flow, in itself, from cold to hot. While no mathematical relationships come directly from the second law, a set of equations can be developed by adding a few assumptions for use in compressor analysis. For a reversible process, entropy, s, can be defined in differential form as

It is recognized that a truly reversible process does not exist in the real world. If it is further recognized that real processes result in an increase in entropy, the second law can be stated.

If work done in a system is distributed over an area, for example, pres sure P is acting through volume v, then in specific notation and in differential form the Equation 2.44 results.

If further AU = AE when the kinetic and potential energies in Equation 2.36 do not change, Equation 2.35 can be rewritten, substituting U for E, changing to the specific notation and putting the equation in differential form.

Combining Equations 2.42, 2.44 and 2.45 yields du = Tds - Pdv

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