Transmission Of Heat Question 223
Question: The rectangular surface of area 8 cm $ \times $ 4cm of a black body at a temperature of $ 127^{o}C $ emits energy at the rate of E per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to $ 327^{o}C $ , the rate of emission of energy will become
[MP PET 2000]
Options:
A) $ \frac{3}{8}E $
B) $ \frac{81}{16}E $
C) $ \frac{9}{16}E $
D) $ \frac{81}{64}E $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {{(Q)} _{Black,body}}=A\sigma T^{4}t $
Therefore $ \frac{Q}{t}\propto $
$ P=A\sigma T^{4} $ Breadth are halved so area becomes one fourth.
Therefore $ \frac{P _{1}}{P _{2}}=\frac{A _{1}}{A _{2}}\times {{( \frac{T _{1}}{T _{2}} )}^{4}} $
Therefore $ \frac{A _{1}}{(A _{1}/4)}\times ( \frac{273+327}{273+127} ) $
Therefore $ P _{2}=\frac{81}{64}E $
BETA
