Question

the specific heat of a gas in a polytropic process is given by

Answer 1

I had an attempt at it and this is what I got: (I used α α as the polytropic index instead of n n) Using: δ Q = n C α d T δQ=nCαdT and d U = n C v d T dU=nCvdT δ Q = d U + δ W n C α d T = n C v d T + P d V n C α △ T = n C v △ T + ∫ P V α V α d V n C α △ T = n C v △ T + P V α ∫ 1 V α d V n C α △ T = n C v △ T + P V α ∫ 1 V α d V n C α △ T = n C v △ T + P V α 1 − α + 1 V − α + 1 n C α △ T = n C v △ T + P V 1 − α + 1 C α = C v + P V n △ T 1 − α + 1 C α = C v + R 1

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