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. `(p)/(alphaK)`
B. `(3alpha)/(pK)`
C. `3pKalpha`
D. `(p)/(3alphaK)`

Answer

D

Explanation

`K=(p)/((-DeltaV//V))rArr(DeltaV)/(V)=(p)/(K)rArr-DeltaV=(pV)/(K)`
Change in volume `DeltaV=gammaVDeltaT`
where , `gamma=` coefficient of volume epansion
Again `,gamma=3alpha`
`alpha` is coefficient of linear expansion
`thereforeDeltaV(3alpha)DeltaTtherefore(pV)/(K)V(3alpha)DeltaTthereforeT=(P)/(3alphaK)`