Question

A uniform pressure P is exerted on all sides of a solid cube at temperature $t^{\circ }C$. 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 is $\alpha$ and the bulk modulus is $\beta$.

• A. $\frac{P}{\alpha \beta }$
• B. $\frac{P\alpha }{\beta }$
• C. $\frac{P\beta }{\alpha }$
• D. $\frac{\alpha \beta }{P}$

Answer 1

The correct option is A

$\frac{P}{\alpha \beta }$

Decrease in volume, $\Delta V=\frac{VP}{\beta }$ ...... (i)
This is to be compensated by an increase in volume by heating through a temperature $\theta$. If $\alpha$ is the coefficient of volume expansion, the increase in volume is given by $\Delta V=\alpha V\theta$ ...... (ii)
Equating (i) and (ii), we get $\theta =\frac{P}{\alpha \beta }$, which is choice (a).