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.
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.
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