For any process, ∆G = ∆H - ∆(TS).
Apply this on reversible adiabatic expansion of perfect gas, since the entropy of system does not change during this process, S is constant so
∆G = ∆H - S∆T
The process is reversible, so
∆G = 0
∆H = S∆T
For perfect gas, assume heat capacity independent of temperature,
∆H = Cp∆T
Cp∆T = S∆T.
∆T is not zero during adiabatic reversible expansion- temperature drops. So divide both sides by ∆T gives
Cp = S
Is this legit? If not where is my mistake? I have a hunch that I did something terribly stupid. The final result seems to be so counter-intuitive because
The Cp and S are constant throughout the process, so at the end of the process the two will still be the same. By measuring Cp, even though your system is not doing adiabatic reversible expansion, you will get S. So we are able to measure S?