Transmission Of Heat Question 248
Question: A sphere at temperature 600K is placed in an environment of temperature is 200K. Its cooling rate is H. If its temperature reduced to 400K then cooling rate in same environment will become
[CBSE PMT 1999; BHU 2001]
Options:
A) (3/16)H
B) (16/3)H
C) (9/27)H
D) (1/16)H
Show Answer
Answer:
Correct Answer: A
Solution:
Rate of cooling $ \propto (T^{4}-T _{0}^{4}) $
Therefore $ \frac{H}{H’}=\frac{(T _{1}^{4}-T _{0}^{4})}{(T _{2}^{4}-T _{0}^{4})}= $
$ \frac{400^{4}-200^{4}}{600^{4}-200^{4}} $ or $ H’=\frac{(16+4)(16-4)H}{(36+4)(36-4)} $
$ =\frac{3}{16}H $
BETA
