Question

A constant pressure $P$ is applied on a cube from all directions. By what amount should its temperature be raised so that its volume remains constant. The bulk modulus of the material of the cube is $K$ and its coefficient of cubical expansion is $\gamma$.

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

Answer 1

The correct option is A $\frac{P}{K\gamma }$

The bulk modulus is given by,
$K=\frac{PV}{\Delta V}\Rightarrow \Delta V=\frac{PV}{K}$

For cubical expansion of the cube,
$V^{\prime }=V(1+\gamma \Delta T)$

$\therefore \Delta V=V\gamma \Delta T$

For volume of the cube to remain constant, the change in volume $\Delta V$ in equations $\left(i\right)$ and $\left(ii\right)$ should be equal.
$\Rightarrow \frac{PV}{K}=V\gamma \Delta T$

$\therefore \Delta T=\frac{P}{K\gamma }$

Hence, $\left(A\right)$ is the correct answer.