1. Tardigrade
  2. Question
  3. Physics
  4. 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 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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 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

Thermal Properties of Matter

Solution:

Due to thermal expansion
$\frac{\Delta V}{V} = 3\alpha \Delta T\,\,....(1)$
Volumetric strain due to external pressure
$\frac{\Delta V}{V} = \frac{P}{K} \,\,.....(2)$
Equating both equations we get
$3\alpha \Delta T = \frac{P}{K} $
$\Rightarrow \Delta T = \frac{P}{3\alpha K}$