Asked by Anonymous
An aluminum beam was brought from the outside cold into a machine shop where the temperature was held at 65 degrees F. After 10 minutes, the beam warmed to 35 degrees F anf after another 10 minutes its temprature was 50 degrees F. Use Newton's Law of Cooling to estimate the beam's initial temperature.
Answers
Answered by
drwls
The differential equation that is obeyed is
M C dT/dt = h A (65-T)
where mass M, specific heat C, film cooling coefficient h and surface area A are constants.
The solution has the form
dT/(65-T) = c dt
-ln(T-65) = c t + a
T-65 = exp (-a -ct)
You have two unknowns constants (a and c) and two equations for T at t = 10 and t = 20 minutes. Once you have a and c you can solve for T when t=0.
M C dT/dt = h A (65-T)
where mass M, specific heat C, film cooling coefficient h and surface area A are constants.
The solution has the form
dT/(65-T) = c dt
-ln(T-65) = c t + a
T-65 = exp (-a -ct)
You have two unknowns constants (a and c) and two equations for T at t = 10 and t = 20 minutes. Once you have a and c you can solve for T when t=0.