Q. An external pressure $P$ is applied on a cube at $0^{\circ}C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :
Solution:
$K = \frac{\Delta P}{\left(-\frac{\Delta V }{V}\right)}$
$\frac{\Delta V}{V} = \frac{P}{K}$
$\therefore V = V_{0} \left(1 + \gamma\Delta t \right)$
$\frac{\Delta V}{V_{0}} = \gamma\Delta t$
$\therefore \frac{P}{K} = \gamma\Delta t $
$\Rightarrow \Delta t = \frac{P}{\gamma K } =\frac{P}{3 \alpha K} $
