Transmission Of Heat Question 321
Question: Three discs A, B and C having radii 2 m, 4 m and 6 m respectively on coated with carbon black on their outer surfaces. The wavelength corresponding to maximum intensities are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are $ Q _{A},,Q _{B} $ and $ Q _{C} $ respectively
Options:
A) $ Q _{A} $ is maximum
B) $ Q _{B} $ is maximum
C) $ Q _{C} $ is maximum
D) $ Q _{A}=Q _{B}=Q _{C} $
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Answer:
Correct Answer: B
Solution:
[b] Idea The radiant power i.e., energy radiated by a body per unit time is given by $ \frac{Q}{t}=A\varepsilon \sigma T^{4} $
$ \Rightarrow $ $ Q\propto AT^{4} $ Also $ {\lambda _{m}}T=\text{constant} $
$ \Rightarrow $ $ Q\propto \frac{A}{{{({\lambda _{m}})}^{4}}} $ Power radiated, $ Q\propto AT^{4} $ and $ {\lambda _{m}}T= $ constant Hence, $ Q\propto \frac{A}{{{({\lambda _{m}})}^{4}}} $ or $ Q\propto \frac{r^{2}}{{{({\lambda _{m}})}^{4}}} $ $ Q _{A}:Q _{B}:Q _{C}=\frac{{{(2)}^{2}}}{{{(3)}^{4}}}:\frac{{{(4)}^{2}}}{{{(4)}^{4}}}:\frac{{{(6)}^{2}}}{{{(5)}^{4}}} $ $ =0.05:0.0625:0.0576 $ i.e., $ Q _{B} $ is maximum. TEST Edge Question related to Kirchhoffs law, Stefan’s law, Newton’s law of cooling and Wien’s displacement law are frequently asked, students are advised, to have better understanding of concept and application of these topics.
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