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A steel ball at an initial pressure of 1.0e5 Pa is heated from 20°C to 120°C while its volume is held constant. Find the pressure inside the ball. Linear expansion coefficient of steel = 12e-6 /°C; bulk modulus of steel = 1.6e11 N/m².

1. 1.0e5 Pa
2. 2.0e8 Pa
3. 1.9e8 Pa
4. 1.6e8 Pa

Correct answer: 1.9e8 Pa

Solution

Holding volume constant requires a compressive pressure K*3*alpha*ΔT ≈ 1.9e8 Pa, which dominates the initial pressure, giving about 1.9e8 Pa.

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