Object in a Temperature Bath with Exponentially Decaying Temperature.
An object with volume V and surface area A is immersed in a large bath, just as modeled in class, however this time the bath temperature varies as a function of time T(t). The external bath , initially at a temperature T0, cools down exponentially: T(t) = T0et. The average heat transfer coefficient between the object and the bath is known: h. Furthermore, there is almost no conductive resistance in the object such that one can assume negligible internal resistance. Determine the temperature of the object as a function of time. [Note: The method of solution for this problem should follow the one derived in class, but with one important and major difference. This will produce a completely different ODE, likely non-homogenous, that will be difficult to solve. If you are unable to find the solution to this type of problem in your DE textbook, you can obtain the solution using modern tools (e.g. Wolfram Alpha, graphing calculator, Mathematica).]