An external pressure P is applied on a cube at 0^o C so that it i… - Vidyadip

MCQ

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

✓
$\frac{P}{{3\alpha K}}$
B
$\;\frac{P}{{\alpha K}}$
C
$\;\frac{{3\alpha }}{{PK}}$
D
$\;3PK\alpha $

✓

Answer

Correct option: A.

$\frac{P}{{3\alpha K}}$

a
As we know , Bulk modulus

$K = \frac{{\Delta P}}{{\left( {\frac{{ - \Delta V}}{V}} \right)}} \Rightarrow \frac{{\Delta V}}{V} = \frac{P}{K}$

$V = {V_0}\left( {1 + \gamma \Delta t} \right)$

$\frac{{\Delta V}}{{{V_0}}} = \gamma \Delta t$

$\therefore \frac{P}{K} = \gamma \Delta t \Rightarrow \Delta t = \frac{P}{{\gamma K}} = \frac{P}{{3\alpha K}}$

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