A black body radiates heat at temperatures ‘T1’ and ‘T2’ (T2 T1). The frequency corresponding to maximum energy is

Question

A black body radiates heat at temperatures ‘T1’ and ‘T2’ (T2 > T1). The frequency corresponding to maximum energy is (A) more at T1 (B) more at T2 (C) equal for T1 and T2 (D) independent of T1 and T2

Tardigrade Admin · Accepted Answer

Energy radiated by the bodies are E1=σ A T14 and E2=σ A T24 ⇒ (E2/E1)=((T2/T1))4>1 [∵ T2>T1] ⇒ E2>E1 or h v2>h v1 or v2>v2 Thus, frequency corresponding to T2 is more.

Q. A black body radiates heat at temperatures ‘ $T_{1}$ ’ and ‘ $T_{2}$ ’ $(T_{2} > T_{1})$ . The frequency corresponding to maximum energy is

more at $T_{1}$

more at $T_{2}$

equal for $T_{1}$ and $T_{2}$

independent of $T_{1}$ and $T_{2}$

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

Q. A black body radiates heat at temperatures ‘T1​’ and ‘T2​’ (T2​>T1​). The frequency corresponding to maximum energy is

more at T1​

more at T2​

equal for T1​ and T2​

independent of T1​ and T2​