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A cube at 0 deg C is subjected to an external pressure P that compresses it uniformly from all sides. The material has bulk modulus K and linear expansion coefficient alpha. To restore the cube to its original volume by heating, by how much must the temperature be raised?

1. P/(3*alpha*K)
2. 3*P*K*alpha
3. P/(alpha*K)
4. 3*alpha/(P*K)

Correct answer: P/(3*alpha*K)

Solution

The fractional volume decrease from pressure, P/K, must be offset by the thermal volume increase 3*alpha*delta_T, giving delta_T = P/(3*alpha*K).

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