The pressure applied from all directions on a cube is P. How much… - Vidyadip

MCQ

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 $\alpha$

✓
$\frac{P}{\alpha \beta}$
B
$\frac{P \alpha}{\beta}$
C
$\frac{P \beta}{\alpha}$
D
$\frac{\alpha \beta}{P}$

✓

Answer

Correct option: A.

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

(a) If coefficient of volume expansion is $\alpha$ and rise in temperature is $\Delta \theta$ then $\Delta V=V \alpha \Delta \theta$
$\Rightarrow \frac{\Delta V}{V}=\alpha \Delta \theta$ Volume elasticity
$\beta=\frac{P}{\Delta V / V}=\frac{P}{\alpha \Delta \theta} \Rightarrow \Delta \theta=\frac{P}{\alpha \beta}$

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