Question

A uniform pressure $P$ is exerted on all sides of a solid cube at temperature $0^{o}C$. In order to bring the volume of the cube to the original volume, the temperature of the cube must be increased by $t^{o}c$. If $\alpha$ is the linear coefficient of thermal expansion and $K$ the bulk modulus of the material of the cube, then $t$ is equal to

• A. $\frac{3P}{K\alpha }$
• B. $\frac{P}{2\alpha K}$
• C. $\frac{P}{3\alpha K}$
• D. $\frac{P}{\alpha K}$

Answer 1

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

$K=P/\Delta v/v$
$\frac{\Delta v}{v}=\frac{P}{K}$
Now, $\frac{\Delta v}{v}=3\frac{\Delta l}{l}$
and $\frac{\Delta l}{l}=\alpha \Delta T$
So, $3\frac{\Delta l}{l}=\frac{P}{K}$
$\Rightarrow 3\alpha t=\frac{P}{K}$
$\Rightarrow t=\frac{P}{3\alpha K}$