A) \[40{}^\circ C\]
B) \[45{}^\circ C\]
C) \[48{}^\circ C\]
D) \[42{}^\circ C\]
Correct Answer: C
Solution :
\[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=K\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right)\] \[\therefore \]\[\frac{80{}^\circ -60{}^\circ }{1}=K\left( \frac{80{}^\circ +60{}^\circ }{2}-30{}^\circ \right)\] \[20=K\times 10\Rightarrow K=\frac{1}{2}\] For next 1 min \[\frac{60{}^\circ -\theta }{1}=\frac{1}{2}\left( \frac{60{}^\circ +\theta }{2}-30{}^\circ \right)\] \[120{}^\circ -2\theta =\frac{60{}^\circ +\theta -60{}^\circ }{2}\] \[240{}^\circ -4\theta =\theta \] \[\Rightarrow \] \[\theta =\frac{240{}^\circ }{5}=48{}^\circ C\]
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