Question

A uniform pressure P is exerted on all sides of a solid cube at temperature t${}^0$ C. By what amount should the temperature of the cube be raised in order to bring its volume back to the original value before the pressure was applied, if the bulk modulus is B and volume coefficient is $\gamma$?

• A. $\frac{\gamma P}{B}$
• B. $\frac{P}{\gamma B}$
• C. $\frac{B}{\gamma P}$
• D. $\frac{1}{\gamma BP}$

Answer 1

The correct option is B $\frac{P}{\gamma B}$

The decrease in volume is
$\Delta V=\frac{VP}{B}$
This is to be compensated by an increase in volume by heating so as to raise its temperature by $\theta$.
If $\gamma$ is the coefficient of volume expansion, the increase in volume is
$\Delta V=\gamma V\theta$
Equating the two equations we get
Amount of temperature raised $\theta =\frac{P}{\gamma B}$