A sample of an ideal gas undergoes an isothermal change between two equilibrium states A and B. Answer the following questions related to the mechanical work involved in the process.
(i) Define mechanical work done by a gas during a quasi-static volume change in terms of the pressure–volume variables.
(ii) State how the magnitude and the sign of the work are related to the area under the P–V curve and to the direction of the volume change.
(iii) If the gas expands isothermally from volume V1 to V2 (V2>V1), describe the qualitative shape of the P–V graph and explain why this shape arises.
(iv) Describe, without performing any numerical calculation, how you would estimate the work graphically if only the initial and final pressures and volumes are known, but the explicit equation of state is not given.