So, I have a basic, very basic, understanding of thermodynamics. I don't take it until next semester. I'm attempting to write a program which plots a temperature over time graph of a room being heated/cooled until a certain threshold is met, the users desired temperature, at which point the temperature will drop at the rooms natural rate of loss.
I am finding it very difficult to get equations together for this. So far this is what I have:
- Room volume
- Temperature inside/outside/desired
- Heater value in kW
- Surface areas of windows/floor/ceiling
- Air density
I would be immensely grateful for any help or guidance, this has been driving me crazy.
Best Answer
Think of it as a resistors in parallel problem.
You have a heat source inside the room and a constant temperature outside (if you assume that the outdoors is infinite and well connected to the walls. Then you have a thermal resistance/area for the wall, ceiling and floor material. Using the total area you have an overall thermal resistance and a temperature difference.
While the heater is running you will have an equilibrium where the temperature difference depends on the thermal resistance of the walls and the outside temperature.
When the heater turns off you will have a certain amount of energy inside (based on the heat capacity of the air and the inner wall material) and a rate of cooling. The only tricky part is that the rate of cooling is proportional to the temperature difference - so if you haven't done calculus yet you might have to approximate a series of time points in a spreadsheet.