A uniform pressure p is exerted on all sides of a solid cube of a material at temprature `t^(@)C`. By what amount should the temperature of the cube be raised in order to bring its original volume back to the value it had before the pressure was applied ? K is the bulk modulus and `alpha` is the coefficient of linear expansion of material of solid cube.

Options

A. `(palpha)/(beta)`
B. `(3palpha)/(beta)`
C. `(p)/(alphabeta)`
D. `(p)/(3alphabeta)`

Answer

D

Explanation

(d) We have `((DeltaV)/(V))_(1)=gammaDeltat=3alpha (Deltal)` (by change in temperature)
and `((DeltaV)/(V))_(2)=(p)/(beta)" "`(by pressure)
`((DeltaV)/(V))_(1)=((DeltaV)/(V))_(2)` or `3alpha(Deltat)=(p)/(beta)`
`therefore Deltat=(p)/(3alphabeta)`