Question

An external pressure $P$ is applied on a cube at $0^{0}C$ 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. $\frac{P}{3\alpha K}$
• B. $\frac{P}{\alpha K}$
• C. $\frac{3\alpha }{PK}$
• D. $3\alpha PK$

Answer 1

The correct option is A

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

Step 1: Given data.

External pressure$=P$

Bulk modulus$=K$

coefficient of linear expansion$=\alpha$

Step 2: Finding raised temperature bringing cube to its original size.

We know that,

Due to thermal expansion.

$\frac{∆V}{V}=3\alpha ∆T$ …$\left(i\right)$

Where, $∆V$is change in volume, $V$ is initial volume and $∆T$ is change in temperature

Also,

Due to external pressure.

$\frac{∆V}{V}=\frac{P}{K}$ ….$\left(ii\right)$

From equation $\left(i\right)$ and $\left(ii\right)$ we get

$3\alpha ∆T=\frac{P}{K}$

$\Rightarrow$$∆T=\frac{P}{3\alpha K}$

Hence, option A is correct.