Question
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 71°C, it is cooling at a rate of 1°C per minute. When does this occur?
Answers
oobleck
Recall the differential equation:
dT/dt = -k(T-A)
So, you want
-1 = -k(71-20)
k = 1/(71-20) = 1/51
Now you know that
T(t) = 20 + (95-20)e^-t/51 = 71
t = 20
dT/dt = -k(T-A)
So, you want
-1 = -k(71-20)
k = 1/(71-20) = 1/51
Now you know that
T(t) = 20 + (95-20)e^-t/51 = 71
t = 20