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# A uniform pressure P is exerted on all sides of a solid cube at  ${\text{t}}^{\text{o}}\text{c}$, by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? (K is bulk modulus and $\alpha$  is coefficient of linear expansion?

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a
K3Pα
b
P3Kα
c
α3KP
d
3KP
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detailed solution

Correct option is B

bulk modullus of a material is K=PΔVV ;  here P is pressure, ΔV is change in volume, V is initial volume ΔVV=PK.........(1)  coefficient of linear expansion is α=Δll.ΔT  ; here Δl change in length; l is initial length; ΔT is change in temperature coefficient of volume expansion is γ=3α ΔVVΔT=3.α ΔVV=3.α.ΔT substitute eqn(1) PK=3.α.ΔT ΔT=P3Kα

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