Question

A uniform pressure $P$ is exerted on all sides of a solid cube. It is heated through $\Delta t$ in order to bring its volume back to the value it had before the application of pressure. Then:

• A. $\Delta t=\frac{P}{B_{\gamma }}$
• B. $\Delta t=\frac{B}{P_{\gamma }}$
• C. $\Delta t=B\gamma P$
• D. $\Delta t=\frac{B_{\gamma }}{P}$

Answer 1

The correct option is A $\Delta t=\frac{P}{B_{\gamma }}$

Modulus of Elasticity $B$ is given as $B=\frac{PV}{\Delta V}$

So change in volume can b e written as $\Delta V=\frac{PV}{B}$

But change in volume can also be written as $\Delta V=V\gamma \Delta t$

Equating both we get $V\gamma \Delta t=PV/B$ or $\Delta t=\frac{P}{B\gamma }$

Option A is correct.