Chapter 8.13, Problem 33MP

Compare the temperatures of your cup of coffee at time $t$

(a) if you add cream and let the mixture cool;

(b) if you let the coffee and cream sit on the table and mix them at time t.

Hints: Assume Newton’s law of cooling (Problem 2.27) for both coffee and cream (where it is law of heating). Combine $n^{\prime }$ units of cream initially at temperature $T_0^{\prime }$ with $n$ units of coffee initially at temperature $T_0,$ and find the temperature at time $t$ in (a) and in (b) assuming that the air temperature remains a constant $T_a$, and that the proportionality constant in the law of cooling is the same for both coffee and cream.