Question

Two spherical black bodies of radii $r_{1}$ and $r_{2}$and with surface temperature $T_{1}$ and $T_{2}$ respectively radiate the same power. Then the ratio of $r_{1}$ and $r_{2}$will be

• A. $\left( \frac{T_{2}}{T_{1}} \right)^{2}$
• B. $\left( \frac{T_{2}}{T_{1}} \right)^{4}$
• C. $\left( \frac{T_{1}}{T_{2}} \right)^{2}$
• D. $\left( \frac{T_{1}}{T_{2}} \right)^{4}$

Answer 1

Answer: (A)

$\left( \frac{T_{2}}{T_{1}} \right)^{2}$

Answer 2

P = A σ T⁴ = 4πr²σ T⁴ ⇒ $P \propto r^{2}T^{4}$ or $r^{2} \propto \frac{1}{T^{4}}$

[As P = constant] ∴ $\frac{r_{1}}{r_{2}} = \left( \frac{T_{2}}{T_{1}} \right)^{2}$