Question #42187

One mole of an ideal gas in a cylinder with a conducting piston of area $A$ undergoes a cyclic process $1 \to 2 \to 3 \to 1$. Process $1 \to 2$ is an isothermal expansion at temperature $T_0$ from volume $V_0$ to $2V_0$. Process $2 \to 3$ is isobaric compression at pressure $P_0$ back to volume $V_0$. Process $3 \to 1$ is isochoric heating back to the initial state 1. The initial pressure is $P_1 = 2P_0$. During the expansion $1 \to 2$, the piston moves through a magnetic field and experiences a retarding magnetic force $F = \frac{\alpha}{V}$, where $\alpha = P_0 V_0 A$. The electrical energy from the resulting eddy currents is entirely dissipated as heat into the gas. The magnetic field is zero during $2 \to 3$ and $3 \to 1$. What is the net heat absorbed by the gas from the external thermostat during the complete cycle?