A) \[\frac{1}{k}\]
B) \[\frac{In\,\,2}{k}\]
C) \[\frac{1}{2k}\]
D) None of these
Correct Answer: B
Solution :
[b] Max. heat loss for temperature change \[={{T}_{b}}-{{T}_{s}}\] \[\frac{dT}{dt}=-k(T-{{T}_{s}})\] \[\int{\frac{dT}{T-{{T}_{s}}}}=-\int{k\,\,dt}\] In \[[T-{{T}_{s}}]_{i}^{{{T}_{s}}}=-kt\] In \[[\frac{{{T}_{f}}-{{T}_{s}}}{{{T}_{i}}-{{T}_{s}}}]=-kt\] \[-In\,\,2=-kt\] \[t=\frac{In\,2}{k}\]
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