# Calculating the amount of heat extracted in a cycle in P-V diagram [closed]

The question goes like this: There's a thermodynamic cycle of an engine, operating with an ideal monoatomic gas. What'll be the amount of heat extracted from the source in a single cycle?

My Approach: The work done by the gas is the area enclosed by the cycle, $$\Delta W = P_0 V_0$$ By the first law of thermodynamics, $$\Delta U = \Delta Q - \Delta W$$ Since, in a cycle $\Delta U = 0$, $$\Delta Q = \Delta W = P_0 V_0$$

But the book says that the answer is $(13/2)P_0V_0$. Where I'm possibly going wrong?

• I think they mean you to calculate "heat exhausted by the engine to the cold bath" not "net heat exchanged with both baths". – Sean E. Lake Feb 11 '17 at 4:29
• You have to calculate the heat exchanged for each process (each line in the graph) and add them up. – Yashas Feb 11 '17 at 5:09