Question

Two spheres of radii $8 \, cm$ and $2 \, cm$ are cooling. Their temperatures are $127 \, ℃$ and $527 \, ℃$ respectively. The ratio of energy radiated by them in the same amount of time is

• A. $0.06$
• B. $0.5$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

Total energy radiated from a body
$Q=A\varepsilon \sigma T^{4}t$
or $\frac{Q}{t} \, \propto AT^{4}$
$\frac{Q}{t} \, \propto r^{2}T^{4}$ ( $\because \, A=4\pi r^{2})$
$\frac{Q_{1}}{Q_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2} \, \left(\frac{T_{1}}{T_{2}}\right)^{4}$
$= \left(\frac{8}{2}\right)^{2} \left(\frac{273 + 127}{273 + 527}\right)^{4} = 1$