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A cube at 0°C is subjected to an external pressure P, producing equal compression on all faces. If the cube has bulk modulus K and coefficient of linear expansion α, by how much must its temperature be increased to restore it to its original dimensions?

1. 3α/(PK)
2. 3PKα
3. P/(3αK)
4. P/(αK)

Correct answer: P/(3αK)

Solution

Pressure causes fractional volume decrease dV/V = P/K. Restoring it by heating needs 3*alpha*dT = P/K, so dT = P/(3*alpha*K).

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