Transmission Of Heat Question 178
Question: If a metallic sphere gets cooled from $ 62^{o}C $ to $ 50^{o}C $ in $ 40^{o}C $ and in the next $ 10\ \min utes $ gets cooled to $ 42^{o}C $ , then the temperature of the surroundings is
[MP PET 1997]
Options:
A) $ 30^{o}C $
B) $ 36^{o}C $
C) $ 26^{o}C $
D) $ 20^{o}C $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{{\theta _{1}}-{\theta _{2}}}{t}=K[ \frac{{\theta _{1}}+{\theta _{2}}}{2}-{\theta _{0}} ] $ In the first 10 minute $ \frac{62-50}{10}=K,[ \frac{62+50}{2}-{\theta _{0}} ] $
Therefore $ 1.2=,K,[56-{\theta _{0}}] $ …. (i) $ \frac{50-42}{10}=K,[ \frac{50+42}{2}-{\theta _{0}} ] $
Therefore $ 0.8=,K,[46-{\theta _{0}}] $ …. (ii) from equations (i) and (ii)$ \frac{1.2}{0.8}=\frac{(56-{\theta _{0}})}{(46-{\theta _{0}})} $
Therefore $ {\theta _{0}}=26{}^\circ C $
BETA
