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An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

1. P/3αK
2. P/αK
3. 3α/P K
4. 3PKα

Correct answer: P/3αK

Solution

The correct option is derived from the relationship between bulk modulus, pressure, and temperature change. To restore the cube to its original size after uniform compression, the temperature must be increased by an amount that compensates for the volume change due to the applied pressure, which is given by the formula P/(3αK).

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