• id: JME-10-N15
• title: Newton's Law of Cooling — Application
• tags: newton, cooling, approximation

For a body cooling in surroundings at temperature $T_s$ with small temperature excess: $dT/dt = -k(T - T_s)$. Solution: $T - T_s = (T_0 - T_s)e^{-kt}$ (exponential decay). For JEE, the practical average form is used: $(T_1 - T_2)/t = k[(T_1 + T_2)/2 - T_s]$, where the body cools from $T_1$ to $T_2$ in time $t$. The constant $k$ is found from one interval and applied to the next. This is derived from Stefan's law for small temperature differences and is an approximation — it works well when $(T - T_s)/T_s$ is small.