Transmission Of Heat Question 117
Question: A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $ T $ , then
[Manipal MEE 1995]
Options:
A) The hollow sphere will cool at a slower rate for all values of $ T $
B) The solid sphere will cool at a faster rate for all values of $ T $ compared to a hollow sphere of the same mass and material
C) Both spheres will cool at the same rate for all values of $ T $ if they have the same emissivity and surface area
D) Both spheres will cool at the same rate only for small values of $ T $
Show Answer
Answer:
Correct Answer: A
Solution:
Rate of cooling $ \frac{\Delta \theta }{t}=\frac{A\varepsilon \sigma (T^{4}-T _{0}^{4})}{mc} $ As surface area, material and temperature difference are same, so rate of loss of heat is same in both the spheres. Now in this case rate of cooling does not depend on mass.
Therefore Rate of cooling $ \frac{\Delta \theta }{t}\propto \frac{1}{m} $ Q $ m _{solid}>m _{hollow} $ . Hence solid sphere will cool fast.
BETA
