Discussion
Which quantity is the specific entropy of an ideal gas proportional to?
Answer: A
For an ideal gas the specific entropy equals the specific heat at constant pressure multiplied by the natural logarithm of the potential temperature, plus an arbitrary constant. This single identification is what makes potential temperature so central to atmospheric thermodynamics, because it means that a surface of constant potential temperature is a surface of constant entropy and that adiabatic reversible motion is confined to such a surface. The arbitrary constant is harmless because only entropy differences ever enter a physical calculation.
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