- #1
fishspawned
- 66
- 16
I am having trouble wrapping my head around a particular problem I am thinking about.
Consider that I have a heating source that I can describe in terms of either degrees Celcius / second or Joules / second, but essentially I am able to determine a fixed heating rate.
Let's say:
dT/dt = 5 degrees / second
If I have an object in a room with a specific ambient temperature, it would also be experience simultaneous cooling, which is determined [i assume] through Newton's Law of Cooling, namely:
T = (To - Troom)e-kt + Troom
Where k is a constant and Troom is the ambient temperature, also fixed.
The issue is how to combine these two things into one equation because with Newton's Law of Cooling, the assumption is that you start from a fixed initial temperature, To. But if it is being heated, then To is going to be changing as it gets warmed up, assuming the heating rate is larger than the cooling rate.
So I am hoping someone can offer some help in how this can be reconciled in some way - or is this simply regulated to hands on testing of the object to see what happens in the real world?
Consider that I have a heating source that I can describe in terms of either degrees Celcius / second or Joules / second, but essentially I am able to determine a fixed heating rate.
Let's say:
dT/dt = 5 degrees / second
If I have an object in a room with a specific ambient temperature, it would also be experience simultaneous cooling, which is determined [i assume] through Newton's Law of Cooling, namely:
T = (To - Troom)e-kt + Troom
Where k is a constant and Troom is the ambient temperature, also fixed.
The issue is how to combine these two things into one equation because with Newton's Law of Cooling, the assumption is that you start from a fixed initial temperature, To. But if it is being heated, then To is going to be changing as it gets warmed up, assuming the heating rate is larger than the cooling rate.
So I am hoping someone can offer some help in how this can be reconciled in some way - or is this simply regulated to hands on testing of the object to see what happens in the real world?