Question

A sample of gas expands from volume $V_1$ to $V_2$. The amount of work done by the gas is greatest when the expansion is

• A. adiabatic
• B. isobaric
• C. isothermal
• D. equal in all above cases

Answer 1

Answer: (B)

The $P$ - $V$ diagram for isobaric, isothermal and adiabatic process of an ideal gas is shown in graph below

In thermodynamics, for same change in volume, the work done is maximum for the curve having maximum area enclosed with the volume axis.
Area enclosed by the curve $\propto$ (Slope of curve)
As shown
(slope) ${}_{\text{isobaric }}<$ (slope) ${}_{\text{isothermal }}<$ (slope) ${}_{\text{adiabatic }}$ $\Rightarrow$ (Area) ${}_{\text{isobaric }}>$ (Area) ${}_{\text{isothermal }}>$ (Area) ${}_{\text{adiabatic }}$
Hence, work done is maximum in isobaric process.