MHT CET · Physics · Thermal Properties of Matter
Two spherical black bodies have radii \(r 1\) and \(r_2\). Their surface temperatures are \(T 1\) and \(T_2\). If they radiate same power then \(\frac{r_2}{r_1}\) is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
\(\frac{Q}{t}=\sigma A T^4\)
i.e. power \(=\sigma A T^4\)
\(\therefore \) for same power
\(\therefore A \propto \frac{1}{T^4}\)
\(\therefore \frac{A_2}{A_1}=\frac{T_1^4}{T_2^4}\)
\(\therefore \frac{4 \pi r_2^2}{4 \pi r_1^2}=\frac{T_1^4}{T_2^4}\)
\(\therefore \frac{r_2}{r_1}=\left(\frac{T_1}{T_2}\right)^2\)
i.e. power \(=\sigma A T^4\)
\(\therefore \) for same power
\(\therefore A \propto \frac{1}{T^4}\)
\(\therefore \frac{A_2}{A_1}=\frac{T_1^4}{T_2^4}\)
\(\therefore \frac{4 \pi r_2^2}{4 \pi r_1^2}=\frac{T_1^4}{T_2^4}\)
\(\therefore \frac{r_2}{r_1}=\left(\frac{T_1}{T_2}\right)^2\)
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