posted by Debbie on .
A cold metal bar at -30 degrees Celsius is submerged in a pool maintained at a temperature of 40 degrees Celsius. Half a minute later, the temperature of the bar is 20 degrees Celsius. How long will it take the bar to attain a temperature of 30 degrees Celsius?
I know that dy/dt=k(y-b) and y(t)=b+Ce^kt
The solution will be of the form
T - 40 = (-70)*exp(-kt)
Note that this satisfies T = -30 when t = 0 and T-> 40 as t -> infinity
Solve for k by using the fact that
T = 20 at t = 30 s.
-20 = -70*exp(-30 t)
exp(-30k) = 0.2857
-30k = -1.253
k = 4.18*10-2
(1/k) = 23.9 seconds
Now solve for t when T = 30 C
I hate this
Doesn't help for me in any thing