A) \[38{}^\circ C\]
B) \[40{}^\circ C\]
C) \[42{}^\circ C\]
D) \[44{}^\circ C\]
Correct Answer: C
Solution :
From Newtons cooling law \[\frac{{{}_{1}}-{{}_{2}}}{t}=K\left( \frac{{{}_{1}}+{{}_{2}}}{2}-26 \right)\] Case\[\text{I:}\] \[\begin{align} & \frac{12}{10}=K\times 30 \\ & K=\frac{12}{10\times 30} \\ \end{align}\] \[=\frac{1}{25}\] Case\[\text{II:}\] \[\frac{50-{{}_{2}}}{10}=K\left( \frac{50+{{}_{2}}}{2}-26 \right)\] \[\begin{align} & \frac{50-{{\theta }_{2}}}{10}=\frac{1}{25}\left( \frac{{{\theta }_{2}}-2}{2} \right) \\ & 250-5{{\theta }_{2}}={{\theta }_{2}}-2 \\ \end{align}\] \[6{{}_{2}}=252\] \[{{}_{2}}=\frac{252}{6}=42{}^\circ C\]
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