Tutoring calculus or differential equations, Newton’s Law of Cooling will surface. The tutor looks at a real-life example.
In yesterday’s post I mention that a casserole dish taken out of the oven cooled from 177C to about 40C during one hour.
Newton’s Law of Cooling can be used to calculate the temp of a cooling object:
Tf = Tiekt
Tf = final temp
Ti = initial temp
k = the constant of cooling (if cooling, k will turn out negative)
t = time (usually in seconds)
For this case, we have t=3600 (3600s in one hour):
40 = 177ek3600
Dividing both sides by 177 gives
Now we ln both sides:
ln0.226 = 3600k
Finally we divide by 3600:
-4.13×10-4 = k
Apparently the cooling constant of the casserole is -4.13×10-4.
Larson, Roland E. and Robert P. Hostetler. Calculus. Toronto: D.C. Heath and Company, 1989.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.