Question

Two solid spheres of radii r₁ and r₂ have surfaces of same nature and are of same material. Both spheres are at same high temperature 'T'. They are allowed to cool under same conditions. Initial rate of heat loss is –

• A. (a) $\left( \frac{r_{2}}{r_{1}} \right)^{2}$
• A. (b) $\left( \frac{r_{1}}{r_{2}} \right)^{2}$
• A. (c)$\sqrt{\frac{r_{1}}{r_{2}}}$
• A. (d) $\sqrt{\frac{r_{2}}{r_{1}}}$

Answer 1

(b)

Since ratio of rate of loss of heat is equal to ratio between rate

of emission, we have

$\frac{Q_{1}}{Q_{2}}$ = $\frac{\varepsilon_{1}}{\varepsilon_{2}}$ = $\frac{eA_{1}\sigma\theta^{4}}{eA_{2}\sigma\theta^{4}}$ = $\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}$ = $\left( \frac{r_{1}}{r_{2}} \right)^{2}$