Newton's law of cooling: $dT/dt = -k(T - T_s)$ where $T_s$ is the surr…

Question

Newton's law of cooling: $dT/dt = -k(T - T_s)$ where $T_s$ is the surrounding temperature. The general solution is:

Accepted Answer

A. $T = T_s + c e^{-kt}$

Substituting $u = T - T_s$ gives $du/dt = -ku$ ⇒ $u = c e^{-kt}$ ⇒ $T = T_s + c e^{-kt}$. As $t 	o \infty$, $T 	o T_s$ (body equilibrates with surroundings).

Answer

$T = T_s + c e^{kt}$

Answer

$T = T_s - ct$

Answer

$T = T_s t + c$