Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2024 (4 May, Shift 2)

Answer: (a)

1. Emissive power $E = e\sigma T^4$; equal $E$ gives $e_1 T_1^4 = e_2 T_2^4$.
2. The emissivity ratio is missing in the question; in the original version $e_1 : e_2 = 1 : 3$.
3. $\left(\dfrac{T_1}{T_2}\right)^4 = \dfrac{e_2}{e_1} = 3 \Rightarrow \dfrac{T_1}{T_2} = 3^{1/4}$
4. So the answer works out to (c) $3^{1/4} : 1$.