Heat and Thermodynamics 2 Question 1
4. 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 $\alpha$ 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
(2017 Main)
(a) $\frac{p}{\alpha K}$
(b) $\frac{3 \alpha}{p K}$
(c) $3 p K \alpha$
(d) $\frac{p}{3 \alpha K}$
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Answer:
Correct Answer: 4. (d)
Solution:
- $K=\frac{p}{(-\Delta V / V)} \Rightarrow \frac{\Delta V}{V}=\frac{p}{K}$
$\Rightarrow-\Delta V=\frac{p V}{K} \Rightarrow \frac{p V}{K}=V(3 \alpha) \Delta T$
$\therefore \quad \Delta T=\frac{p}{3 \alpha K}$
