Transmission Of Heat Question 219
Question: A spherical black body with a radius of $ 12\ cm $ radiates $ 440\ W $ power at $ 500\ K $ . If the radius were halved and the temperature doubled, the power radiated in watt would be
[IIT 1997 Re-Exam]
Options:
225
450
900
D) 1800
Show Answer
Answer:
Correct Answer: D
Solution:
Radiated power by blackbody $ P=\frac{Q}{t}=A\sigma T^{4} $
Therefore $ P\propto AT^{4} $
$ \propto r^{2}T^{4} $
Therefore $ \frac{P _{1}}{P _{2}}={{( \frac{r _{1}}{r _{2}} )}^{2}},{{( \frac{T _{2}}{T _{1}} )}^{4}} $
Therefore $ \frac{440}{P _{2}}={{( \frac{12}{6} )}^{2}},{{( \frac{500}{1000} )}^{4}} $
Therefore $ P _{2}=1760,W\approx 1800,W $
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