Understanding Newton's Law of Cooling: Definition, Equation, and Application

[Arcthor]

If the temperature of an object with temperature T(t) is place in a room with the ambient temperature T_a, Newtons Law of Cooling is defined as dT / dt = k (T(t) - T_a), correct?

This implies we would need a negative k-value. Wouldn't the equation therefore be described better if T(t) and T_a changed place? As in: dT / dt = k (T_a - T(t))

What am I missing?

 

[russ_watters]

The convention is somewhat arbitrary, but I think it makes sense for heat loss to be negative and heat gain to be positive.

 

[Chestermiller]

The firm of the equation I am familiar with is the one that you suggested.

Chet