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 $=12\times {10}^{-6}{}^{\circ }{C}^{-1}$ 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 at a constant volume.

So the stress arises

$\frac{P}{\frac{\Delta V}{V}}=B$

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

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

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

$=1.6\times 3\times 12\times {10}^{11}\times {10}^{-6}\times {10}^2$

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