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Newton's law of cooling: $dT/dt = -k(T - T_s)$ where $T_s$ is the surrounding temperature. The general solution is:
A$T = T_s + c e^{-kt}$
B$T = T_s + c e^{kt}$
C$T = T_s - ct$
D$T = T_s t + c$
Answer & Solution
Correct 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 $t \to \infty$, $T \to T_s$ (body equilibrates with surroundings).
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