Question

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

• A. $\frac{P}{\alpha K}$
• B. $\frac{P}{3\alpha K}$
• C. $3PK\alpha$
• D. $\frac{3\alpha }{PK}$

Answer 1

The correct option is B $\frac{P}{3\alpha K}$

We know that :
$\frac{\Delta V}{V}=3\alpha \Delta T,K=\frac{P}{\frac{\Delta V}{V}}$
Due to thermal expansion
$\frac{\Delta V}{V}=3\alpha \Delta T$
Volumertric strain due to external pressure
$\frac{\Delta V}{V}=\frac{P}{K}$
Equating both equations we get
$3\alpha \Delta T=\frac{P}{K}\Delta T=\frac{P}{3\alpha K}$

Final answer: (c)