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