Physics - Heat & Thermo Question with Solution | TestHub

The given relation is

$\text{P}=\frac{\alpha {\text{T}}^2}{\text{V}}\therefore \text{V}=\frac{\alpha {\text{T}}^2}{\text{P}}$

As pressure is kept constant,$\text{dV}=\left(\frac{2\alpha \text{T}}{\text{P}}\right)\text{dT}$

$\text{W}=\int \text{P}·\text{dV}=\underset{{\text{T}}_0}{\overset{{\text{2T}}_0}{\int }}\text{P}\left(\frac{2\alpha \text{T}}{\text{P}}\right)\text{dT}=2\alpha {\left[\frac{{\text{T}}^2}{2}\right]}_{{\text{T}}_0}^{{\text{2T}}_0}=3\alpha {\text{T}}_0^2$