A) \[{{45}^{o}}C\]
B) \[{{42.85}^{o}}C\]
C) \[{{40}^{o}}C\]
D) \[{{38.5}^{o}}C\]
Correct Answer: B
Solution :
Key Idea: As the body cools down, its rate of cooling slows down. From Newtons law of cooling when a hot body is cooled in air, the rate of loss of heat by the body is proportional to the temperature difference between the body and its surroundings. Given, \[{{\theta }_{1}}={{60}^{o}}C,\,{{\theta }_{2}}={{50}^{o}}C,\,\theta ={{25}^{o}}C\]. \[\therefore \] Rate of loss of heat = K (Mean temp. - Atmosphere temp.) where K is coefficient of thermal conductivity. \[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=K\left( \frac{{{\theta }_{1}}-{{\theta }_{2}}}{2}-\theta \right)\] \[\frac{60-50}{10}=K\left( \frac{60+50}{2}-25 \right)\] \[\Rightarrow \] \[K=\frac{1}{30}\] Also putting the value of K, we have \[\frac{50-{{\theta }_{3}}}{10}=\frac{1}{30}\left( \frac{50+{{\theta }_{3}}}{2}-25 \right)\] \[\Rightarrow \] \[{{\theta }_{3}}={{42.85}^{o}}C\] Note: For Newtons law of cooling to hold good, temperature difference between the body and its surroundings should not be large.
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