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 it. The temperature should be raised by :

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

Answer 1

Answer: (A)

$\frac{P}{3 \alpha K}$

Answer 2

$K = \frac{\Delta P}{\left(-\frac{\Delta V }{V}\right)}$
$\frac{\Delta V}{V} = \frac{P}{K}$
$\therefore V = V_{0} \left(1 + \gamma\Delta t \right)$
$\frac{\Delta V}{V_{0}} = \gamma\Delta t$
$\therefore \frac{P}{K} = \gamma\Delta t$
$\Rightarrow\Delta t = \frac{P}{\gamma K } =\frac{P}{3 \alpha K}$