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EEJ MAIN Physics QUESTION #7052
Question 1
A cube at $0^\circ\text{C}$ is subjected to external pressure $P$, causing equal compression on all sides. If $K$ is the material's bulk modulus and $\alpha$ is the linear expansion coefficient, what temperature increase is required to restore the cube to its original volume?
  • $3 PK \alpha$
  • $\frac{P}{3\alpha K}$✔️
  • $\frac{P}{\alpha K}$
  • $\frac{3\alpha}{PK}$
Correct Answer Explanation

From the definition of Bulk Modulus $K$:

$\frac{\Delta V}{V} = \frac{P}{K}$ (Volume strain due to pressure)

From thermal expansion, the increase in volume is:

$\frac{\Delta V}{V} = \gamma \Delta T = 3\alpha \Delta T$

To restore the original size, the thermal expansion must equal the pressure compression:

$3\alpha \Delta T = \frac{P}{K} \implies \Delta T = \frac{P}{3\alpha K}$