First slide

Thermal expansion

Question

A steel ball initially at a pressure of 1.0 × 10⁵ Pa is heated from 20°C to 120°C keeping its volume constant. Find the pressure inside the ball. Coefficient of line expansion of steel = 12 × 10^-6/°C and bulk modulus steel = 1.6 × 10¹¹ N/m²

Easy

A

2.5 × 10⁸ Pa
B

5.8 × 10⁸ Pa
C

3.5 × 10⁸ Pa
D

4.2 × 10⁸ Pa

Solution

Bulk modulus $\large k=\frac {P}{-\left ( \frac {\Delta V}{V} \right )}$
$\large \frac {\Delta V}{V}=\frac {P}{k}=\gamma \Delta t\left [ \therefore \gamma=\frac {\Delta V}{V\Delta t} \right ]$ $\large \therefore \Delta t=\frac {P}{k\gamma}$
$\large P=k\gamma \Delta t=3k\alpha \Delta t=3(1.6\times 10^{11})(12\times 10^{-6})(100)$
$\large =5.8\times 10^8Pa$

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