Problem 1 Consider situation discussed in class where an obj

Problem 1. Consider situation discussed in class where an object of temperature T(t) is cooling/heating in environment of constant temperature TE. (a) From Newton?s law we have that T = K(TE - T), t > 0; T(0) = T0. Show how to find the solution of this ODE. (b) More generally in heating/cooling it is reasonable to expect the temperature difference d(t) = T(t) - TE to satisfy d=f(d), where the function f is unknown. Assume that d is small, and Taylor expand f. Keep only the first two terms. Then on physical grounds, argue why the first term should vanish. Finally, compare/contrast this new ODE to the one arising from Newton?s law.

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