Transmission Of Heat Question 119
Question: A body initially at 80o C cools to 64o C in 5 minutes and to 52o C in 10 minutes. The temperature of the body after 15 minutes will be
[UPSEAT 2000; Pb. PET 2004]
Options:
A) 42.7 o C
B) 35 o C
C) 47 o C
D) 40 o C
Show Answer
Answer:
Correct Answer: A
Solution:
According to Newton law of cooling $ \frac{{\theta _{1}}-{\theta _{2}}}{t}=K,[ \frac{{\theta _{1}}+{\theta _{2}}}{2}-{\theta _{0}} ] $ For first process : $ \frac{(80-64)}{5}=K[ \frac{80+64}{2}-{\theta _{0}} ] $ …(i) For second process : $ \frac{(80-52)}{10}=K[ \frac{80+52}{2}-{\theta _{0}} ] $ …(ii) For third process : $ \frac{(80-\theta )}{15}=K[ \frac{80+\theta }{2}-{\theta _{0}} ] $ ?(iii) On solving equation (i) and (ii) we get $ K=\frac{1}{15} $ and $ {\theta _{0}}=24{}^\circ C $ . Putting these values in equation (iii) we get $ \theta =42.7{}^\circ C $
BETA
