Question

Two spheres made of same substance have diameters in the ratio 1 : 2. Their thermal capacities are in the ratio of

• A. (a) 1 : 2
• A. (b) 1 : 8
• A. (c) 1 : 4
• A. (d) 2 : 1

Answer 1

(b)

Thermal capacity = Mass × Specific heat

Due to same material both spheres will have same specific heat

∴Ratio of thermal capacity $= \frac{m_{1}}{m_{2}} = \frac{V_{1}\rho}{V_{2}\rho}$

$= \frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}} = \left( \frac{r_{1}}{r_{2}} \right)^{3} = \left( \frac{1}{2} \right)^{3} = 1:8$