Question

The ratio of radii of two spheres of same material is $1 : 4$, then the ratio of their heat capacities is

• A. $\frac{1}{4}$
• B. $\frac{1}{16}$
• C. $\frac{1}{32}$
• D. $\frac{1}{64}$

Answer 1

Answer: (D)

$\frac{1}{64}$

Answer 2

Heat capacity $H=m s=\frac{4}{3} \pi r^{3} \rho s$ For same material, density $\rho$ and specific heat $s$ are same, so heat capacity $H \propto r^{3}$ Hence, the ratio of heat capacities is $\frac{H_{1}}{H_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{3}=\left(\frac{1}{4}\right)^{3}=\frac{1}{64}$