Newtons Cooling Law

Newton's Law of cooling states the the rate at which the temperature  
  of a bnody decrease is proportional to the temperature difference between the body and its surroundings  
\[\frac{dT_b}{dt}=-k(T_s -T_b)\]
If the temperature of the surroundings is higher than the temperature of the body then the temperature of the body Will increase at a rate  
\[\frac{dT_b}{dt}=k(T_s -T_b)\]
Integration of the first equation with initial temperature  
\[T_b (t) = T_s - e^{-kt}(T_s-T_b)\]
/ This is an exponential decay curve.

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