Question

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

Answer 1

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

$K=\frac{P}{\frac{△V}{16}}$ (by definition) ____(1)

also, $V_f=V_0(1+r△T)$

Where $r=3\propto$ _____(2)

$△V=V_f-V_0$

$\Rightarrow △V=V_f-V_0=V_{0}r△T$

Putting in (1)

$K=\frac{P}{\frac{V_{0}r△T}{V_0}}=\frac{P}{r△T}$

$\Rightarrow △T=\frac{P}{Kr}=\frac{P}{3K\propto }$ using (2)