The work done by an ideal gas of 2 moles in increasing its volume from V to 2 V at constant temperature T is…
The work done by an ideal gas of 2 moles in increasing its volume from V to 2 V at constant temperature T is W . The work done by an ideal gas of 4 moles in increasing its volume from V to 8 V at constant temperature $\frac{\mathrm{T}}{2}$ is
W
2 W
3 W
4 W
Solution
$\begin{aligned} & \quad \mathrm{n}_1=2 \text { moles, vol }=\mathrm{V} \text { to } 2 \mathrm{~V}, \mathrm{~T}_1=\mathrm{T}, \mathrm{W}_1=\mathrm{W} \\ & \mathrm{n}_2=4 \text { moles, vol }=\mathrm{V} \text { to } 8 \mathrm{~V}, \mathrm{~T}_2=\frac{\mathrm{T}}{2}, \mathrm{~W}_2=?\end{aligned}$
The work done by ideal gas at constant temperature is $\mathrm{W}=\mathrm{nRT} \ln \frac{\mathrm{V}_2}{\mathrm{~V}_1}$
$\begin{aligned} & \therefore \quad \mathrm{W}_1=\mathrm{W}=2 \mathrm{RT} \ln \frac{2 \mathrm{~V}}{\mathrm{~V}}=2 \mathrm{RT} \ln 2 \\ & \mathrm{~W}_2=4 \mathrm{R} \cdot \frac{\mathrm{T}}{2} \ln \frac{8 \mathrm{~V}}{\mathrm{~V}}=2 \mathrm{RT} \ln 8=6 \mathrm{RT} \ln _2\end{aligned}$
$=3\left(2 \mathrm{RT} \ln ^2\right)=3 \mathrm{~W}$