A) 4 min
B) 6 min
C) 5 min
D) 8 min
Correct Answer: B
Solution :
From the Newton?s law of cooling. Rate of cooling \[\propto \] difference in temperature. \[\frac{dT}{dt}\propto \Delta \theta \] \[\Rightarrow \] \[\frac{dT}{dt}=K\Delta \theta \] In first case, \[dT=61-59=2\] \[\Delta \theta =50-30=20\] \[dt=4\,\min ,\] \[\therefore \] \[K=\frac{1}{\Delta \theta }\left( \frac{dT}{dt} \right)=\frac{2}{30\times 4}=\frac{1}{60}\] For second case, \[dT=2\] \[\Delta \theta =50-30=20\] \[\therefore \] \[dt=\frac{1}{K}\,\left( \frac{dT}{d\theta } \right)=\frac{2}{\frac{1}{60}\times 20}=6\,\min \]You need to login to perform this action.
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