A) \[(T-{{T}_{S}})\]
B) \[{{(T-{{T}_{S}})}^{2}}\]
C) \[{{(T-{{T}_{S}})}^{1/2}}\]
D) \[{{(T-{{T}_{S}})}^{4}}\]
Correct Answer: A
Solution :
By Stefan's law, \[\frac{dT}{dt}=\frac{A\varepsilon \sigma }{mc}[{{T}^{4}}-T_{0}^{4}]\] When the temperature difference between the body and its surrounding is not very large ie,\[T={{T}_{0}}=\Delta T\]then\[{{T}^{4}}-T_{0}^{4}\]maybe approximated as \[4T_{0}^{3}\Delta T\]. Hence, \[\frac{dT}{dt}=\frac{A\varepsilon \sigma }{mc}4T_{0}^{3}\Delta T\] \[\Rightarrow \] \[\frac{dT}{dt}\propto \Delta T\] ie, if the temperature of the body is not very different from surrounding, rate of cooling is proportional to temperature difference between the body and its surrounding. This law is called Newton's law of cooling.
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