Change in entropy of an ideal gas during thermodynamic cycle

[Elvis 123456789]

Homework Statement

An ideal gas with adiabatic index γ is taken around a complete thermodynamic cycle consisting of three steps. Starting at point A, the pressure is increased at constant volume V1 from P1 to P2 at point B. From point B to point C, the gas is allowed to expand adiabatically from volume V1 and pressure P2 to volume V2 and the original pressure P1. Finally, from point C to point A, the volume of the gas is decreased at constant pressure P1 back to the original volume V1.

a) Make a PV diagram of the complete cycle.

b) For each step of the cycle, determine the change in the entropy of the gas. Sum your results to find the total entropy change for the whole cycle. Note that every step is reversible.

c) Use the adiabatic relations to eliminate the pressure from your result for part b. Show that the resulting expression gives a total entropy change for the complete cycle equal to zero.

Homework Equations

ΔS = C_P*ln(V/V₀) + C_V*ln(P/P₀)

The Attempt at a Solution

I did part a.) which is in the attachment, as well as my work so far for part b.). I'm not sure how to express the heat capacities in terms of the adiabatic index... any hints?

 

[Chestermiller]

What you have is correct so far. How do P1, P2, V1, and V2 have to be related for the adiabatic expansion?