Transmission Of Heat Question 166
Question: A bucket full of hot water cools from $ 75^{o}C $ to $ 70^{0}C $ in time $ T _{1} $ , from $ 70^{o}C $ to $ 65^{o}C $ in time $ T _{2} $ and from $ 65^{o}C $ to $ 60^{o}C $ in time $ T _{3} $ , then
[NCERT 1980; MP PET 1989; CBSE PMT 1995; KCET 2003; MH CET 1999]
Options:
A) $ T _{1}=T _{2}=T _{3} $
B) $ T _{1}>T _{2}>T _{3} $
C) $ T _{1}<T _{2}<T _{3} $
D) $ T _{1}>T _{2}<T _{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
According to Newton’s law of cooling Rate of cooling µ Mean temperature difference
Therefore
$ \frac{\text{Fall in},\text{temperature}}{\text{Time}}\propto ( \frac{{\theta _{1}}+{\theta _{2}}}{2}-{\theta _{0}} ) $
Q $ {( \frac{\theta _{1}+\theta _{2}}{2} )_1}>{( \frac{\theta _1+\theta _2}{2} )_2}$ >$( \frac{{\theta _1}+{\theta _2}}2)_3 $
Therefore $ T _{1}<T _{2}<T _{3} $
BETA
