Q: A uniform pressure ‘P’ is exerted on all sides of a solid cube at temperature 0°C. In order to bring the volume of the cube to the original volume, the temperature of the cube must be increased by t°C. If α is the linear coefficient and K be the bulk modulus of the material of the cube, then t is equal to

(a) $ \displaystyle \frac{3P}{K \alpha} $

(b) $ \displaystyle \frac{P}{2 K \alpha} $

(c) $ \displaystyle \frac{P}{3 K \alpha} $

(d) $ \displaystyle \frac{P}{K \alpha} $

Ans: (c)

Sol: $\large K = \frac{P}{\Delta V/V}$

$\large \Delta V = \frac{P V}{K}$ …(i)

As t is the required increase in temperature,

ΔV = γ V t ….(ii)

From (i) & (ii)

$\large \gamma V t = \frac{P V}{K}$

$\large t = \frac{P }{\gamma K}$

$\large t = \frac{P }{3 \alpha K}$