I was doing problems on the application of differential equations. This question popped out there.
It is a simple Separable Equation with initial and end condition given. I found out the temperature profile and plotted it.
Then, when the ambient temperature is changed, obviously the constant of integration has to be adjusted suitably right? I did it with the initial condition.
Now my question is will the constant of proportionality(k) in Newton's law remain same as found with the previous ambient temperature? Why?
Assuming k remains constant, I proceed with the problem and found the solution
But I can't get the intuition behind it. What determines the value of k? I found out k value by using an information pertaining to a different ambient temperature in the first place.
If I tweak the ambient temperature and the k value remains same, then is it safe to assume that all the cooling follows the same exponential path?