An ideal gas undergoes this process: In a p V diagram point 1 starts at (V1,P1)

Question

An ideal gas undergoes this process:

In a p V diagram point 1 starts at (V1,P1) moves to (V1, P2) then to (V2,P2) then (V2,P1) then ends back at (V1,P1)

Where P2>P1 and V2>V1

This is just an ideal Carnot cycle engine where for example the expression for the heat expelled for the section from (V2,P2) to (V2,P1) equals (f/2)*V2(P1-P2)

Ok so here is the question

A) Compute the Change in internal energy for the Gas

B) Compute the net work done on the Gas

C) Compute the net heat added to the Gas

D) Compute the entropy change of the Gas

Express all answers in terms of P1,P2,V1,V2 and indicate the sign of your answer

Explanation / Answer

A) Internal energy is a state function. Since initial state = final state

=> delta E = 0

B) Work done =- P*dV = - P2*(V2-V1) - P1(V1 - V2) = (P2 - P1)(V1 - V2)

C) Heat = - Work done = (P2 - P1)(V2 - V1)

D) Again entropy is a state function

So, delta S = 0

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