## Newtons Cooling Law

Newton's Law of cooling states the the rate at which the temperature\[T_b\]

of a bnody decrease is proportional to the temperature difference between the body and its surroundings \[T_s\]

.\[\frac{dT_b}{dt}=-k(T_s -T_b)\]

.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

\[T_0\]

gives \[T_b (t) = T_s - e^{-kt}(T_s-T_b)\]

/ This is an exponential decay curve.