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A cube at temperature  00C  is compressed equally from all sides by an external pressure P. By x amount its temperature be raised to bring it back to the size it had before the external pressure was applied (The bulk modulus of the material of the cube is K and the coefficient of linear expansion is α ). Then value of ‘x’ is

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a

P/Kα

b

P/3Kα

c

3πα/K

d

3K/P

answer is B.

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Detailed Solution

Bulk modulus K=PΔV/V=PVΔV _________(1) ΔV=γVΔT=3αVT ___________(2)From equation 1 and 2 K=P3αT     or  T=P3αK
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A cube at temperature  00C  is compressed equally from all sides by an external pressure P. By x amount its temperature be raised to bring it back to the size it had before the external pressure was applied (The bulk modulus of the material of the cube is K and the coefficient of linear expansion is α ). Then value of ‘x’ is