@lee, thanks for the pointer. I knew the solution to the simple thermal equation was of the same form as an electronic RC network - a T0 x e^ -kt /RC kind of equation. But your link also reminded me of two things.
- The other side of the equation is a difference between the current temperature and the terminal temperature (final temp of the evaporator coil), not an absolute temperature. This needs to change in my graphing.
- And if we were dealing with absolute temperatures for thermodynamics, they would have to be expressed in either Kelvin (or if we want to be obtuse, Rankine).
@pswired, I’m guessing you are right. There really are two or even three different domains to this problem.
- At t=0, the dominating process is the compressor cooling the evaporator coil down from the ambient temp, to near its terminal temperature, with a fairly sort time constant.
- As that is happening the evaporator coil begins transferring heat out of the moving air, again at a rate determined by the temperature difference between the coil and air temperature. This curve likely has a much longer time constant than the first process. Eventually the air cooling hits a terminal temperature based on an equilibrium where the coil based cooling, limited by the differential between the intake temp and the coil, is balanced by heat leaking into the system from various sources.
- The system either achieves its cooling goal and turns off, or on a very hot day, stays on running in an equilibrium, that is slowly perturbed by changes in the ambient temperature and the intake temperature.
ps: I have a constant speed air handler and single stage compressor.