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A cube initially at 0°C is subjected to the same external pressure P on all its faces, causing it to be compressed. How much must its temperature be increased so that the cube regains its original size? The bulk modulus of the cube material is B and its coefficient of linear expansion is α.

1. P/(Bα)
2. P/(3Bα)
3. 3α/B
4. 3B/P

Correct answer: P/(3Bα)

Solution

Pressure produces volumetric strain dV/V = P/B (compression). Heating gives volumetric expansion dV/V = 3 alpha dT. Setting 3 alpha dT = P/B gives dT = P/(3 B alpha).

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