An external pressure P is applied on a cube at `0^(@)C` so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and `alpha` 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

Options

A. `(3alpha)/(PK)`
B. `3PK alpha`
C. `(P)/(3alphaK)`
D. `(P)/(alphaK)`

Answer

C

Explanation

`K=(DeltaP)/(((-DeltaV)/(V))) rArr (DeltaV)/(V)=(P)/(K)`
`V=V_(0)(1+gamma Delta t)`
`(DeltaV)/(V_(0))=gamma Delta t " " (P)/(K)=gamma Delta t rArr Delta t= (P)/(gammaK)=(P)/(3alphaK)`