Properties Of Solids And Liquids Question 457
Question: A sphere of density p, specific heat capacity c and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to
Options:
A) $ \frac{c}{r^{3}\rho } $
B) $ \frac{1}{r^{3}\rho c} $
C) $ 3r^{3}\rho c $
D) $ \frac{1}{r\rho c} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ [ \frac{-dT}{dr} ]=\frac{A}{mc}[ T-T _{0} ]=\frac{4\pi r^{2}}{\rho \times \frac{4}{3}\pi r^{3}c}[ T-T _{0} ] $
$ \therefore [ \frac{-dT}{dr} ]\propto \frac{1}{\rho rc} $
