Exercise · ZW-NEWTONS-LAW-OF-COOLING-008 · ★★☆ Intermediate
With \(k=0.25\) per minute, in how many minutes does the difference \(T-T_a\) fall to \(1/e\) of its initial value?
Choose one option.
Show answer
- C. \(4\)
Explanation
\(T-T_a=(T_0-T_a)e^{-kt}\) equals \(1/e\) times the initial value when \(kt=1\), that is, \(t=1/k=4\).
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 \(k>0\).
\[T'=-k\,(T-T_a)\;\Longrightarrow\; T(t)=T_a+(T_0-T_a)\,e^{-kt}\]
More practice problems: newton's law of cooling
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