Two spheres ' $\mathrm{S}_{1}$ ' and ' $\mathrm{S}_{2}$ ' have same radii but temperatures $\mathrm{T}_{1}$…

Two spheres ' $\mathrm{S}_{1}$ ' and ' $\mathrm{S}_{2}$ ' have same radii but temperatures $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ respectively. Their emissive power is same and emissivity is in the ratio $1: 4$. Then the ratio of $\mathrm{T}_{1}$ to $\mathrm{T}_{2}$ is
  1. $\sqrt{2}: 1$
  2. $1: 2$
  3. $2: 1$
  4. $1: \sqrt{2}$

Solution

Emissive power $P=\sigma \mathrm{e} T^{4}$ $\begin{array}{l} \therefore \sigma e_{1} T_{1}^{4}=\sigma e_{2} T_{2}^{4} \\ \frac{T_{1}^{4}}{T_{2}^{4}}=\frac{e_{2}}{e_{1}}=4 \\ \therefore \frac{T_{1}}{T_{2}}=\sqrt{2} \end{array}$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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