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A uniform pressure ‘P’ is exerted on all sides of a solid cube at temperature t°C . By what amount should the temperature of the cube be raised in order to bring back to its original volume, it had before the pressure was applied. (The bulk modulus and
coefficient of volume expansion of the material are B and $γ$ respectively).

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$\frac{PB}{γ}$

$\frac{γ}{PB}$

$\frac{Pγ}{B}$

$\frac{P}{γB}$

answer is D.

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Detailed Solution

$\frac{Δv}{v} = γt = \frac{P}{B}$

$B = \frac{- ΔP}{\frac{ΔV}{V}}$

$ΔV = \frac{- P}{B} V$ .....(i)

${ΔV}_{thermal} = (V) (γ) (ΔT)$ .....(ii)

$\Rightarrow (\frac{P}{B}) V = V (γ) (ΔT)$

$\Rightarrow ΔT = \frac{P}{Bγ}$

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