Two identical cylinders each contain the same amount of the same ideal gas with

Question

Two identical cylinders each contain the same amount of the same ideal gas with the same initial temperature, T_low. The gas in the first cylinder undergoes an isovolumetric pressure increase and reaches a final temperature of T_high. The gas in the second cylinder undergoes an isobaric expansion reaching the same final temperature, T_high. What is the ratio of the change of entropy of the gas in the first cylinder to the change of entropy of the gas in the second cylinder? (DeltaS_1/DelataS_2 = ?)

Explanation / Answer

Here, change in entropy of gas in first cylinder isovolumetric = S1 = Cv ln (T2 / T1)

                                                                                                         = Cv ln (Thigh / Tlow)

=>   change in entropy of gas in second cylinder isobaric = S2 = Cp ln (T2 / T1)

                                                                                                      =   Cp ln (Thigh / Tlow)

=> Ratio ,   S1/S2     = (Cv ln (Thigh / Tlow)) / (Cp ln (Thigh / Tlow))

                                      = Cv / Cp

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