The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume $?$ The volume elasticity of the cube is $\beta $ and the coefficient of volume expansion is $\alpha $
Diffcult
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(a) If coefficient of volume expansion is $\alpha $ and rise in temperature is $\Delta \theta $ then $\Delta V = V\alpha \Delta \theta $$\Rightarrow $ $\frac{{\Delta V}}{V} = \alpha \Delta \theta $
Volume elasticity $\beta = \frac{P}{{\Delta V/V}}$ $ = \frac{P}{{\alpha \Delta \theta }}$==> $\Delta \theta = \frac{P}{{\alpha \beta }}$
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