An ideal gas expands isothermally from volume V 1 to V 2 and then it is adiabatically compressed back to its original volume V 1 . The initial and final pressures of the gas are P 1 and P 3 respectively and the net work done by the gas is W , then

Step-by-step solution

The two processes are shown in the following P-V diagram: For iothermal process: P 1 V 1 = P 2 V 2 i.e., P 1 = V 2 V 1 P 2 For adiabatic process: P 3 V 1 γ = P 2 V 2 γ i.e. P 3 = V 2 V 1 γ P 2 As γ > 1 , hence P 3 > P 1 Further, as slope of adiabatic curve is greater than that of isothermal process curve, adiabatic curve will lie above the isothermal curve. That is, area under adiabatic curve > area under isothermal curve i.e., Negative work > Positive work i.e., W < 0