A) \[28{}^\circ C\]
B) \[25{}^\circ C\]
C) \[30{}^\circ C\]
D) \[22{}^\circ C\]
Correct Answer: A
Solution :
[a] According to Newton's law of cooling, \[\left[ \frac{{{\theta }_{1}}-{{\theta }_{2}}}{t} \right]=K\left[ \left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} \right)-{{\theta }_{0}} \right]\] so that \[\left[ \frac{60-40}{7} \right]=K\left[ \left( \frac{60+40}{2} \right)-10 \right]\] \[\Rightarrow K=\frac{1}{14}\] (i) Now if after cooling from \[40{}^\circ C\]to 7 min the temperature of the body becomes 0, according to Newton's law of cooling, \[\left[ \frac{40-\theta }{7} \right]=K\left[ \left( \frac{40+\theta }{2} \right)-10 \right]\] Which in the light of Eq. (i), i.e., \[K=(1/14)\], gives \[\left[ \frac{40-\theta }{7} \right]=\frac{1}{14}\left[ \left( \frac{20+\theta }{2} \right) \right]\] \[160-4\theta =20+\theta ;\theta =28{}^\circ C\]
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