The figure displays the variation of the internal energy U with the volume V of 2.0 mol of an ideal gas in a cyclic process abcda . The temperatures of the gas at b and c are 500 K and 300 K respectively. Determine the net heat absorbed by the gas during the process. (Take R = 8.3 J K ⁻¹ mol ⁻¹ and 2 = 0.693 )

Step-by-step solution

For an ideal gas, the internal energy U depends only on its temperature T . From the given U-V graph, we can identify the thermodynamic processes: Process a b : U is constant, which implies T is constant. This is an isothermal expansion at T_a = T_b = 500 K . Process b c : V is constant. This is an isochoric process. Process c d : U is constant, which implies T is constant. This is an isothermal compression at T_c = T_d = 300 K . Process d a : V is constant. This is an isochoric process. For a cyclic process, the n