Question

A black body radiates heat at temperatures ‘$T_1$’ and ‘$T_2$’ $(T_2 > T_1)$. The frequency corresponding to maximum energy is

• A. more at $T_1$
• B. more at $T_2$
• C. equal for $T_1$ and $T_2$
• D. independent of $T_1$ and $T_2$

Answer 1

Answer: (B)

Energy radiated by the bodies are
$E_{1}=\sigma A T_{1}^{4}$ and $E_{2}=\sigma A T_{2}^{4}$
$\Rightarrow \,\,\, \frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}>1 \,\,\,\left[\because T_{2}>T_{1}\right]$
$\Rightarrow \,\,\, E_{2}>E_{1}$
or $\,\,\, h v_{2}>h v_{1}$ or $v_{2}>v_{2}$
Thus, frequency corresponding to $T_{2}$ is more.