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Question

An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

A
3PKα
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B
P3αK
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C
PαK
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D
3αPK
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Solution

The correct option is B P3αK
K=PVV0 (by definition) -----(1)

Also, Vf=V0(1+rT)

where r=3α ----- (2)

V=VfV0

=V0rT

Putting in (1)

K=PV0rTV0=PrT

T=PKr=P3Kα [using (2)]


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