Exercise · ZW-NEWTONS-LAW-OF-COOLING-001 · ★☆☆ Basic
Solve \(T'=-0.1\,(T-20)\) with \(T(0)=80\).
Choose one option.
Show answer
- B. \(T=20+60e^{-0.1t}\)
Explanation
With \(T_a=20\) and \(T_0=80\): \(T=T_a+(T_0-T_a)e^{-kt}=20+60e^{-0.1t}\).
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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- ZW-NEWTONS-LAW-OF-COOLING-008 With k=0.25 per minute, in how many minutes does the difference T-T_a fall to 1/e of its initial va…
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