Q: A uniform pressure p is exerted on all sides of a solid cube at temperature t°C. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied ? The coefficient of volume expansion of the cube is γ and the bulk modulus is B.
(a) $ \displaystyle \frac{p}{\sqrt2 \gamma\ B} $
(b) $ \displaystyle \frac{p}{2 \gamma\ B} $
(c) $ \displaystyle \frac{2 p}{ \gamma\ B} $
(d) $ \displaystyle \frac{ p}{ \gamma\ B} $
Ans: (d)
Sol: $B = \frac{p}{\Delta V/V} $
$\frac{\Delta V}{V} = \frac{p}{B}$
$ \gamma \Delta T = \frac{p}{B}$