Transmission Of Heat Question 126
Question: A hot metallic sphere of radius $ r $ radiates heat. It’s rate of cooling is
Options:
A) Independent of $ r $
B) Proportional to $ r $
C) Proportional to $ r^{2} $
D) Proportional to $ 1/r $
Show Answer
Answer:
Correct Answer: D
Solution:
Rate of cooling $ R _{C}=\frac{d\theta }{dt}=\frac{A\varepsilon \sigma (T^{4}-T _{0}^{4})}{mc} $
Therefore $ \frac{d\theta }{dt}\propto \frac{A}{V}\propto \frac{r^{2}}{r^{3}} $
Therefore $ \frac{d\theta }{dt}\propto \frac{1}{r} $
BETA
