Transmission Of Heat Question 225
Question: Two spherical black bodies of radii $ r _{1} $ and $ r _{2} $ and with surface temperature $ T _{1} $ and $ T _{2} $ respectively radiate the same power. Then the ratio of $ r _{1} $ and $ r _{2} $ will be
[KCET 2001; UPSEAT 2001]
Options:
A) $ {{( \frac{T _{2}}{T _{1}} )}^{2}} $
B) $ {{( \frac{T _{2}}{T _{1}} )}^{4}} $
C) $ {{( \frac{T _{1}}{T _{2}} )}^{2}} $
D) $ {{( \frac{T _{1}}{T _{2}} )}^{4}} $
Show Answer
Answer:
Correct Answer: A
Solution:
For black body, $ P=A\varepsilon \sigma T^{4} $ . For same power $ A\propto \frac{1}{T^{4}} $
Therefore $ {{( \frac{r _{1}}{r _{2}} )}^{2}}={{( \frac{T _{2}}{T _{1}} )}^{4}} $
Therefore $ \frac{r _{1}}{r _{2}}={{( \frac{T _{2}}{T _{1}} )}^{2}} $
BETA
