A sample of ideal gas (Degree of freedom f= 5) is heated at constant pressure. lf an amount 140 J of heat is supplied to the gas, the work done by the gas is

Suppose the sample contains n moles. Also suppose the volume changes from ${\mathrm{V}}_1 \mathrm{to} {\mathrm{V}}_2$ and the temperature changes from ${\mathrm{T}}_{1 }\mathrm{to} {\mathrm{T}}_2$.

The heat supplied is

        $∆\mathrm{Q} = ∆\mathrm{U} + \mathrm{P}∆\mathrm{V} = ∆\mathrm{U} + \mathrm{nR}∆\mathrm{T} = ∆\mathrm{U} + \frac{2∆\mathrm{U}}{\mathrm{f}}$

The change in internal energy is

$∆\mathrm{U} = \mathrm{n}\frac{\mathrm{f}}{2}\mathrm{R}({\mathrm{T}}_2-{\mathrm{T}}_1) = \frac{\mathrm{f}}{2}\mathrm{Rn}({\mathrm{T}}_2-{\mathrm{T}}_1)$

       = $\frac{\mathrm{f}}{2+\mathrm{f}}∆\mathrm{Q} = \frac{140\mathrm{J}}{1.4} = 100 \mathrm{J}$

The work done by the gas is $∆\mathrm{W} = ∆\mathrm{Q} - ∆\mathrm{U} = 140 \mathrm{J} - 100 \mathrm{J} = 40 \mathrm{J}$