Question

A steel ball initially at a pressure of $1.0\times {10}^{5}Pa$ is heated from ${20}^{\circ }C$ to ${120}^{\circ }C$ keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel $=12\times {10}^{-6}{/}^{\circ }C$ and bulk modulus of steel $=1.6\times {10}^{11}N/m^2$.

Answer 1

The ball tries to expand its volume. But it is kept in the same volume. So it is kept at a constant volume.

So the stress arises is defined as:

$\frac{P}{\left(\frac{\Delta V}{V}\right)}=B$

$\Rightarrow P=B\frac{\Delta V}{V}=B\times \gamma \Delta \theta$

Substiting the values in above relation:

$P=B\times 3\alpha \Delta \theta$

$=1.6\times {10}^{11}\times {10}^{-6}\times 3\times 12\times {10}^{-6}\times (120-20)$

$=57.6\times {19}^7\approx 5.8\times {10}^{8}pa$