From the following p -V diagram, an ideal gas undergoing a change of state from A to B . Four different processes I, II, III and IV as shown in the figure may lead to same change of state.

Step-by-step solution

The internal energy U of an ideal gas is a state function, which depends only on the temperature T of the gas. For an ideal gas, the internal energy is given by U = f 2 nRT , where f is the degrees of freedom. Since the change of state is from A to B in all four processes, the initial state (P_A, V_A, T_A) and the final state (P_B, V_B, T_B) are the same for all paths. The change in internal energy U is given by U = U_B - U_A = f 2 nR(T_B - T_A) . Because T_A and T_B are fixed for all four processes, the change in