I am going to use Uo for u nought
A cup of coffee has a temperature of Uo when freshly poured. Then it has cooled to 60 C after 1 min and to 40 C after 2 min. Also the room temperature is 20 C. The temperature u(t) of the coffee at time t changes at a rate proportional to the difference of its temperature and the room temperature: du/dt = -k (u-20) for a constant k>0
Treating k and Uo as fixed parameters, calculate the constant k
I have done similar problems but the initial temperature was given so then I could use seperable equations. Not sure how to go about this I keep running into two variables without a system to solve.
Any help would be greatly appreciated.
Yeah. I got that, but then using initial conditions I would have:
60 = ce^-k + 20 and 40 = ce^-2k + 20
I am still left with c and a k in both of them. If I was given initial temp I would lose the e^k and just be left with the c. That's where my confusion is.