An external pressure P is applied on a cube atm `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. `(3 alpha )/(PK)`
B. `3 PK alpha`
C. `(P)/(3 alpha K)`
D. `(P)/(alpha K)`

Answer

C

Explanation

Bulk modulus `B = - (P )/((Delta V )/(V))`
`therefore P =- B xx (Delta V )/(V)`
But `Delta V = 3 alpha V Delta T`
`therefore Delta T`
`therefore P =-B xx (3 alpha V Delta T )/(-V)`
`therefore P = + B xx 3 alpha Delta T`
`therefore Delta T = (P)/(3 alpha B)`
But here B is k.
`therefore Delta T = (P)/(3 alpha K)`