## 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.