On each surface of a solid cube, a uniform pressure p is applied. Calculate the temperature rise of the solid cube so that its volume remains unaltered. Given, the coefficient of volume expansion of the material of the cube =gamma and its bulk modulus of elasticity = B.

On each surface of a solid cube, a uniform pressure p is applied. Calc

1.	On each surface of a solid cube, a uniform pressure p is applied. Calculate the temperature rise of the solid cube so that its volume remains unaltered. Given, the coefficient of volume expansion of the material of the cube =gamma and its bulk modulus of elasticity = B.
Answer» Solution :LET the initial volume of the cube be V and the change in volume DUE to the applied pressure be `DeltaV.` Hence, BULK modulus of elasticity, `"" B=p/((DeltaV)/V) " or, " DeltaV=(pV)/B.` `THEREFORE` Due to the pressure applied the present volume of the cube `=(V-DeltaV)`. Suppose with the rise in temperature by t, the reduced volume increases by `DeltaV` so that the cube regains its initial volume. `therefore "" DeltaV=(V-DeltaV)gammat=(V-(pV)/B)gammat=((B-p)/B)Vgammat` or, `"" (pV)/B=((B-p)/B)gammaVt " or, " t=p/((B-p)gamma).`