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An external pressure P is applied on a cube at $0^{\circ} C$ 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

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$\frac{3 α}{P K}$

$3 P K α$

$\frac{P}{3 α K}$

$\frac{P}{α K}$

answer is C.

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Detailed Solution

$K = \frac{Δ P}{(\frac{- Δ V}{V})} \Rightarrow \frac{Δ V}{V} = \frac{P}{K}$

Also $\frac{Δ V}{V} = 3 α Δ t$

From the above equations we get $Δ t = \frac{P}{3 α K}$

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