Q. The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$
A) $\frac{P}{\alpha\beta}$
B) $\frac{P\alpha}{\beta}$
C) $\frac{P\beta}{\alpha}$
D) $\frac{\alpha\beta}{P}$
Explanation
(a) If coefficient of volume expansion is $\alpha$ and rise in temperature is $\mathrm{\Delta}\theta$ then $\mathrm{\Delta}V = V\alpha\mathrm{\Delta}\theta \Rightarrow \frac{\mathrm{\Delta}V}{V} = \alpha\mathrm{\Delta}\theta$
Volume elasticity $\beta = \frac{P}{\mathrm{\Delta}V/V} = \frac{P}{\alpha\mathrm{\Delta}\theta} \Rightarrow \mathrm{\Delta}\theta = \frac{P}{\alpha\beta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.