Question

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

Answer 1

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).

Accordingly, rate of change in temperature T, `(dT)/dt` would be proportional to `T-T_a` where `T_a` is the ambient temperature.

The differential equation in this case would be `(dT)/dt= -k(T-T_a)`

Since the body which is cooling would obviously be at a higher temperature than its surroundings `d(T)/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`