Q.

A uniform pressure P is exerted on all sides of a solid cube at  toc, 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 α  is coefficient of linear expansion?

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a

K3Pα

b

P3Kα

c

α3KP

d

3KP

answer is B.

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Detailed Solution

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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