A uniform pressure .P. is exerted on all sides cube at temperature `t^(0)C`. By what amount should the temperature of the cube be raised in order to bring its volume back to the volume it had before the pressure was applied, if the bulk modulus and coefficient of volume expansion of the material are B and `gamma` respectively.

Explanation

A by definition fo bulk modulus
`B= - V((DeltaP)/(DeltaV))`, with increase in pressure
decrease in volume of the cube will be given by
`-DeltaV=(VP)/(B)`, (as `DeltaP=P`)
Now with rise in temperature due to thermal expansion, volume increases so if .`Deltatheta`. is the rise in temperature then
`DeltaV=V gamma Delta theta ("as "gamma=(DeltaV)/(V Deltatheta))`
As the volume of the cube remains constant
`(VP)/(B) =Vgamma Delta theta rArr Delta theta =(P)/( gammaB)`