A) \[{{T}_{1}}={{T}_{2}}={{T}_{3}}~\]
B) \[{{T}_{1}}>{{T}_{2}}>{{T}_{3}}\]
C) \[{{T}_{1}}<{{T}_{2}}<{{T}_{3}}\]
D) \[{{T}_{1}}>{{T}_{2}}<{{T}_{3}}\]
Correct Answer: C
Solution :
According to Newton?s law of cooling Rate of cooling \[\propto \] Mean temperature difference \[\Rightarrow \,\,\frac{Fall\,\,in\,\,temperature}{Time}\,\,\propto \,\,\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right)\] \[\because \,\,\,\,{{\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} \right)}_{1}}\,\,>\,\,{{\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} \right)}_{2}}\,\,>\,{{\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} \right)}_{3}}\] \[\Rightarrow \,\,\text{ }{{T}_{1}}<\text{ }{{T}_{2}}<\text{ }{{T}_{3}}\]
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