Question

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

• A. $\frac{P}{\alpha K}$
• B. $\frac{P\alpha }{K}$
• C. $\frac{PK}{\alpha }$
• D. $\frac{2K}{P}$

Answer 1

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

$K=\frac{-PV}{\Delta V_1}$

$-\Delta V_1=\frac{PV}{K}$

Let us suppose change in volume be $\Delta V_2$

when change in temperature is $\Delta T$

$\Delta V_2=V\alpha \Delta T$

For no change in volume after raising temperature,

$\Delta V_1+\Delta V_2=0$

$\frac{PV}{K}=V\alpha \Delta T$

$\Delta T=\frac{P}{\alpha K}$