Q 11-10-125JEE MainJEE Main 2017 (2 Apr)Easy
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:
Answer: (B) $\dfrac{P}{3\alpha K}$
The pressure reduces the volume by the fraction
$$\frac{\Delta V}{V} = \frac{P}{K}$$
Heating by $\Delta T$ increases the volume by the fraction $\gamma\Delta T = 3\alpha\Delta T$. To restore the original size,
$$3\alpha\,\Delta T = \frac{P}{K} \;\Rightarrow\; \Delta T = \frac{P}{3\alpha K}$$
Solution by Sreeraj P, M.Sc Physics