An external pressure $P$ is applied on a cube at $0^{\circ} \mathrm{C}$ 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 :

(C) $\frac{\mathrm{P}}{3 \alpha \mathrm{~K}}$

(A) $\frac{3 \alpha}{\mathrm{PK}}$

(D) $\frac{\mathrm{P}}{\alpha \mathrm{K}}$

JEE Main · 2017 · 02 Apr 2017 · Offline · Elasticity & SHM

An external pressure

P

is applied on a cube at

0^{\circ} 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 :

(A) $\frac{3 α}{PK}$
(B) $3 PK α$
(C) $\frac{P}{3 α K}$ ✓ Correct
(D) $\frac{P}{α K}$

Answer: (C)

Solution

Pressing the cube with pressure

P

gives a volume strain

\frac{Δ V}{V} = - \frac{P}{K}

. To wipe out that shrinkage by warming, thermal expansion must supply an equal and opposite volume strain. Since the coefficient of volume expansion is

3 α

, a rise

Δ T

produces

3 α Δ T

. Setting the two equal,

3 α Δ T = \frac{P}{K}

, so

Δ T = \frac{P}{3 α K}

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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