Question

The heat $(Q)$ supplied to a solid, which is otherwise thermally isolated from its surroundings, is plotted as a function of its absolute temperature, $\theta$. It is found that they are related by the equation, $Q=a \theta^{2}+b \theta^{4}$. ( $a, b$ are constants). The heat capacity of the solid is :

• A. $a \frac{\theta^{3}}{3}+b \frac{\theta^{5}}{5}$
• B. $a \theta+b \theta^{3}$
• C. $a \frac{\theta}{3}+b \frac{\theta^{5}}{5}$
• D. $2 a \theta+4 b \theta^{3}$

Answer 1

Answer: (D)

The heat capacity of the solid is :
$\frac{d Q}{d \theta}=2 a \theta+4 b \theta^{3}$