Question

A uniform pressure p is exerted on all sides of a solid cube at temperature $t^{0}C$. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube y and the bulk modulus is B.

• A. $\frac{p}{\sqrt{2yB}}$
• B. $\frac{p}{2yB}$
• C. $\frac{2p}{yB}$
• D. $\frac{p}{yB}$

Answer 1

The correct option is D $\frac{p}{yB}$

We know that

$B=\frac{-\Delta P}{\frac{\Delta V}{V}}$

Let the initial volume be $V$. Then

$\Delta V=\frac{-P}{B}V$

Expansion to get same volume as initial

$=-\Delta V=\frac{P}{B}V$

We know that thermal volume expansion

$\Delta V_{thermal}=\left(V\right)\left(y\right)\left(\Delta T\right)$

Here $\Delta T=\Delta t^{o}C;-\Delta V=\Delta V_{thermal}$

So, $\left(\frac{P}{B}\right)V=V\left(y\right)\left(\Delta T\right)\Rightarrow \frac{P}{By}=\Delta t$

There is an increment of $\frac{P}{yB}$ in temperature to get same volume as initial