Q88 / 90 · JEE Main 2017 (02 Apr) · Physics

An external pressure $P$ is applied on a cube at $0 ° C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $α$ 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:

Solution

B = \frac{- P}{(\frac{d V}{V})}

\frac{d V}{V} = \frac{- P}{B}

d V = \frac{- P V}{B}

Δ V = V γ Δ T \frac{Δ V}{V} = γ Δ T

\frac{Δ V}{V} = 3 α Δ T

K = \frac{P}{\frac{Δ V}{V}} = \frac{P}{3 α Δ T}

Δ T = \frac{P}{3 α k}

Hence, the correct answer is option: 'B'.