Exercise · ZW-NEWTONS-LAW-OF-COOLING-010 · ★★★ Advanced
In Newton's model, a body cooling from \(T_0>T_a\): when does it reach exactly \(T_a\)?
Choose one option.
Show answer
- D. Never in finite time: it only approaches \(T_a\)
Explanation
\(T-T_a=(T_0-T_a)e^{-kt}\) is positive for all \(t\) and only tends to \(0\) as \(t\to\infty\). It never crosses below \(T_a\) either.
Review the concept: Newton's law of cooling
States that the temperature \(T\) of a body, with initial value \(T_0\), changes at a rate proportional to its difference from the ambient temperature \(T_a\), with constant \(k>0\).
\[T'=-k\,(T-T_a)\;\Longrightarrow\; T(t)=T_a+(T_0-T_a)\,e^{-kt}\]
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