Question

Assertion: Work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion, adiabatically. Reason: Temperature remains constant in isothermal expansion and not in adiabatic expansion

For an ideal gas, the equation of state is the ideal gas relation PV = µRT. For a fixed amount of the gas i.e. given µ, there are thus, only two independent variables, say P and V or T and V. The pressure-volume curve for a fixed temperature is called an isotherm. The thermodynamic state variables are of two kinds: extensive and intensive. Extensive variables indicate the 'size' of the system. Intensive variables such as pressure and temperature do not. To decide which variable is extensive and which intensive, think of a relevant system in equilibrium, and imagine that it is divided into two equal parts. The variables that remain unchanged for each part are Intensive.

The isothermal diagram of a gas at three different temperatures T₁, T₂ and T₃, is shown in the given figure. Then

Derive the work done during the isothermal Process?