Question

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 β and the coefficient of volume expansion is The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ?

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

Answer 1

Answer: (A)

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

Answer 2

Change in volume due to rise in temperature $\Delta V = V\alpha\Delta\theta$

$\therefore$ volumetric strain $= \frac{\Delta V}{V} = \alpha\Delta\theta$

But bulk modulus ⇒$\beta = \frac{\text{stress}}{\text{strain}} = \frac{P}{\alpha\Delta\theta}$ $\therefore\Delta\theta = \frac{P}{\alpha\beta}$