MHT CET · Physics · Thermal Properties of Matter
Two spherical black bodies have radii ' \(r_1\) ' and ' \(r_2\) '. Their surface temperatures are ' \(\mathrm{T}_1\) ' and ' \(\mathrm{T}_2\) '. If they radiate same power, then \(\frac{\mathrm{r}_2}{\mathrm{r}_1}\) is
- A \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\)
- B \(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\)
- C \(\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^2\)
- D \(\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2\)
Step-by-step Solution
Detailed explanation
\( P_1 = P_2 \) \( 4\pi r_1^2 \sigma T_1^4 = 4\pi r_2^2 \sigma T_2^4 \)
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