Transmission Of Heat Question 112
Question: A black metal foil is warmed by radiation from a small sphere at temperature T and at a distance $ d $ . It is found that the power received by the foil is `P’. If both the temperature and the distance are doubled, the power received by the foil will be
[MP PMT 1997]
Options:
A) 16P
B) 4P
C) 2P
D) P
Show Answer
Answer:
Correct Answer: B
Solution:
Energy received per second i.e., power $ P\propto (T^{4}-T _{0}^{4}) $
Therefore $ P\propto T^{4} $
$ (\because ,T _{0}«T) $ Also energy received per sec (p)$ \propto \frac{1}{d^{2}} $ (inverse square law)
Therefore $ P\propto \frac{T^{4}}{d^{2}} $
Therefore $ \frac{P _{1}}{P _{2}}={{( \frac{T _{1}}{T _{2}} )}^{4}}\times {{( \frac{d _{2}}{d _{1}} )}^{2}} $
Therefore $ \frac{P}{P _{2}}={{( \frac{T}{2T} )}^{2}}\times {{( \frac{2d}{d} )}^{2}}=\frac{1}{4} $
Therefore $ P _{2}=4P. $
BETA
