Uniform pressure p is exerted on all sides of a solid cube at temperature t   ° C . By what amount should the temperature be raised in order to bring the volume back to that it had been before the pressure was applied? (Linear expansivity of the material of the cube is α and the bulk modulus of elasticity is β )

Step-by-step solution

Given that Uniform pressure = p temperature = t   ° C Linear expansivity of the material of the cube = α Bulk modulus of elasticity = β Let volume expansion coefficient γ = 3 α Let change in temperature = ∆ t Change in volume with temperature is given by ∆ V = γ V ∆ t ∴     γ = 3 α ⇒     ∆ V V = 3 α ∆ t So Δ V V 1 = γ Δ t = 3 α   Δ t (by change in temperature) and Δ V V