Question

A cube at temperature $0^{o}C$ is compressed equally from all sides by an external pressure $P$. By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied. The bulk modulus of the material of the cube is $B$ and the coefficient of linear expansion is $\alpha$.

• A. $P/B\alpha$
• B. $P/3B\alpha$
• C. $3\pi \alpha /B$
• D. $3B/P$

Answer 1

Answer: (B)

$P/3B\alpha$

Bulk modulus $B=\frac{-P}{\left(\Delta V/V\right)}=\frac{-PV}{\Delta V}$ .......(1)
and $\Delta V=\gamma V\Delta T=3\alpha V.T$ or $\frac{-V}{\Delta V}=\frac{1}{3\alpha .T.}$ .....(2)
From eqs. $\left(1\right)$ and $\left(2\right)$, $B=P/(3\alpha .T)$ or $T=\frac{P}{3\alpha B}$