Uniform pressure p is exerted on all sides of a solid cube at...

Given that&

Uniform pressure $= p$

temperature $= t ° C$

Linear expansivity~of the material of the cube$= \alpha$

Bulk modulus of elasticity~$= \beta$

Let volume expansion coefficient~$\gamma = 3\alpha$

Let change in temperature~$= ∆ t$

Change in volume~with temperature is given by

$∆ V = \gammaV ∆ t$

$∴ \gamma = 3\alpha$

$⇒ \dfrac{∆ V}{V} = 3\alpha ∆ t$

So~ \left(\dfrac{\Delta V}{V}\right)1 = \gamma\Deltat = 3\alpha\left(\Deltat\right)$~(by change in temperature)</p></blockquote><blockquote><p>and \left(\dfrac{\Delta V}{V}\right)2 = \dfrac{p}{β}$ (by pressure)

$∴ \left(\dfrac{\Delta V}{V}\right)1 = \left(\dfrac{\Delta V}{V}\right)2$

$⇒ 3\alpha\left(\Deltat\right) = \dfrac{p}{β}$

$⇒ \Deltat = \dfrac{p}{3\alpha\beta}</p></blockquote>$