Question

You pour a cup of coffee. when its poured, it is 130 F above room temperature, so we will say that difference D=130 F. 3 minutes later, it has cooled to D=117 F above room temperature. As the coffee cools, the instantaneous rate of change of D with respect to time t minutes is directly proportional to D. Write a differential equation which states this relationship.

Answer 1

dT/dt = -C(T - To) ,
where C is a positive constant and To is room tempoerature.

C is approximately 3.3 degrees per minute per degree C, but you would have to solve the differential equation and fit the data point get the exact value of C.