A cup of coffee cools according to Newton's law of cooling, T(t) = T_ env + (T_0 - T_…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

A cup of coffee cools according to Newton's law of cooling, T(t)=Tenv+(T0−Tenv) e−kt,T(t) = T_{\text{env}} + (T_0 - T_{\text{env}})\,e^{-kt}, with room temperature Tenv=20 °CT_{\text{env}} = 20\,\text{°C}, initial temperature T0=90 °CT_0 = 90\,\text{°C}, and cooling constant k=0.050 min−1k = 0.050\,\mathrm{min^{-1}}. Find the rate of cooling dT/dt\mathrm{d}T/\mathrm{d}t at t=20 mint = 20\,\mathrm{min}, taking kk to be constant over the interval.

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