Question

Two spherical bodies $A$ (radius $6cm)$ and $B\left(radius18cm\right)$ are at temperature $T_1$ and $T_2$ respectively. The maximum intensity in the emission spectrum of $A$ is at $500nm$ and in that of $B$ is at $1500nm$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$?

Answer 1

${\lambda }_{m}T=constant,{\lambda }_A{T}_A={\lambda }_B{T}_B$
Now the rate of total energy radiated $E=\sigma A{T}^4$.

$\frac{E_A}{E_B}={\left(\frac{R_A}{R_B}\right)}^2\times {\left(\frac{{\lambda }_A}{{\lambda }_2}\right)}^4$

$={\left(\frac{6}{12}\right)}^2\times {\left(\frac{1500}{50}\right)}^4$

$=9$