# What is c in Newton's Law of Cooling?

Accordingly, rate of change in temperature T, $\frac{\mathrm{dT}}{\mathrm{dt}}$ would be proportional to $T - {T}_{a}$ where ${T}_{a}$ is the ambient temperature.
The differential equation in this case would be $\frac{\mathrm{dT}}{\mathrm{dt}} = - k \left(T - {T}_{a}\right)$
Since the body which is cooling would obviously be at a higher temperature than its surroundings $d \frac{T}{\mathrm{dt}}$ would be negative, hence if k is a positive constant of proportionality, then the right hand side of DE would have a negative sign because $T - {T}_{a} > 0$