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Prove that a reversible adiabatic process cannot also be isothermal for T > 0.
Solution
When a system with two independent thermodynamic co-ordinates undergoes a reversible
adiabatic change of state then we can specify one thermodynamic co-ordinate for the final state
but not two , because change in entropy = S2-S1= 0, i.e. S is fixed . Thus a reversible adiabatic
process can't be isothermal because such a process will fix both T and S and it is impossible.

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