Transmission Of Heat Question 213
Question: Two spheres $ P $ and $ Q $ , of same colour having radii $ 8\ cm $ and $ 2\ cm $ are maintained at temperatures $ 127^{o}C $ and $ 527^{o}C $ respectively. The ratio of energy radiated by $ P $ and $ Q $ is
[MP PMT 1994]
Options:
A) 0.054
B) 0.0034
C) 1
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
Total energy radiated from a body $ Q=A\varepsilon \sigma T^{4}t $
Therefore $ Q\propto AT^{4}\propto r^{2}T^{4} $ (Q $ A=4\pi r^{2}) $
Therefore $ \frac{Q _{P}}{Q _{Q}}={{( \frac{r _{P}}{r _{Q}} )}^{2}},{{( \frac{T _{P}}{T _{Q}} )}^{4}}={{( \frac{8}{2} )}^{2}},{{{ \frac{(273+127)}{(273+527)} }}^{4}}=1 $
BETA
