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?
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 won't solve the problem but I will tell you why you are wrong.
The question asks to find the heat extracted from the source,your reasoning says heat extracted from the source is equal to total work done by the system in a single cycle.
This is clearly against 2nd law of thermodynamics that you cannot convert all of the heat taken from the source to work.
So whats wrong?
Heat extracted from the source is not equal to heat added to the system during the whole process ,because some of the heat extracted from the source is wasted and released to the surrounding.