A system consisting of n moles of an ideal gas with molar specific heat at const

Question

A system consisting of n moles of an ideal gas with molar specific heat at constant pressure C_P undergoes two reversible processes. It starts with pressure P_i and volume V_i, expands isothermally, and then contracts adiabatically to reach a final state with pressure P_i and volume 3V_i. (a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 60. (You do not need to solve Problem 60 to answer this question.) A sample consisting of n moles of an ideal gas undergoes a reversible isobaric expansion from volume V_i to volume 3V_i. Find the change in entropy of the gas by calculating integral ^f_i dQ/T, where dQ = nC_P dT.

Explanation / Answer

(a) ds=dq/T

dq=nRTln(vb/va)

vb=3va

ds=nRln(3)

(b) Answer to question 60 indicates taht it is an isobaric expansion which is reverse of the process. So basically we are expecting to have the same value in the change of entropy. The entropy does not depend on pressure, since the change in volume in both the processes is three times so due to the entropy's dependnece on volume, change will be same in both the processes.

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