Write expressions in terms of the temperature T1, T2, T3, and T4 for the entropy change in each step of the following process for an ideal monatomic gas:
a) Reversible adiabatic expansion from T1P1V to T2P2V'
b) Irreversible heating at constant volume from T2P2V' to T3P3V'
c) Reversible adiabatic compression from T3P3V' to T4P4V
d) Irreversible cooling at constant volume from T4P4V to T1P1V. Prove that the total entropy change for the cycle is 0.
Please provide explanation, work, and formulas that were used to solve this problem including each of the steps.


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