In an adiabatic process for a diatomic gas, the pressure P and temperature T are related as P proportional to T^C. Find the value of C.

Correct answer: 7/2

Solution

Adiabatic: TV^(gamma-1) = const. PV=nRT -> V=nRT/P. Substituting: T*(nRT/P)^(gamma-1)=const -> T*(T/P)^(gamma-1)=const -> T^gamma/P^(gamma-1)=const -> P^(gamma-1)=T^gamma/const -> P proportional to T^(gamma/(gamma-1)). For diatomic gas gamma=7/5: C = gamma/(gamma-1) = (7/5)/(2/5) = 7/2.

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