I am looking at air conditioners and heaters. The impression I get is that 25 BTUs will heat or cool 1 sq ft. of space by looking at how many BTUs they have and how many sq ft. they say they can heat or cool. The 5000 BTU models say about 200 sq ft, the 10000 models say about 400 sq ft.
However, this doesn’t take into account cubic feet (which may not matter since alot of places have universal 8 ft ceilings), and it doesn’t take into account how much you want the temperature to go up or down. A 10000 BTU heater when it is 35 out may be good but not when it is -20 outside.
So is there some universal calculation that shows how many BTUs you need to increase of decrease the temperature of one sq. ft of space by one degree?
Also would initial temperature have any effect on how much energy was required? Would raising the temperature by 1 degree in a 25 degree room be harder than raising it by one degree in a 70 degree room? I don’t know for sure, since heat is a measure of vibrational energy you’d assume the amount of extra vibration that corresponds to an increase in 1 degree would be the same whether you are going from 25-26 or from 70-71 degrees.
I can’t answer most of your questions (thermodynamics always did give me the willies), but I can say this. When you want to size a heater for a room (and I assume AC as well) you get the volume of the room in cubic feet and multiply it by some factor. The multiply factor is 1 for the most highly insulated, tightest room you can imagine, and 10 if the room is basically a barn. Guestimate how well sealed your room is thermally (somewhere around 4 is probably realistic for most rooms) and multiply accordingly.
For example, a 10x20’ room would be 200 sq feet, 10x20x8 = 1600 cubic feet
1600*4 = 6400 = pretty close to the 5000 BTU unit.
This formula at least accounts for rooms that don’t have 8’ ceilings.
Thermodynamics didn’t give me the willies, though it was over ten years ago.
Assuming that the room is perfectly insulated, it would take the same energy to raise the temperature of the room 1 degree at 25 and at 75.
Energy = mass * Heat Coefficient * change in Temp
The Heat Coefficient will be the same for gaseous air at all temps, and the mass will be close to the same.
In a real world, though, you will be losing heat from the room to the outside world. The amount of heat you lose is proportional to the difference in temperature inside the room and outside it. (It also depends upon the surface area of the walls and the insulation, but those are the same in your example above.)
Once you raise the temperature of the room, the job of the heater is to replace the heat lost to the ambient world.
Say it is zero degrees outside. A heater would have to work three times as hard to maintain a 75 degree climate in the room as to maintain a 25 degree.
This isn’t quite true. The specific heats of real gasses change with temperature. However, for this purpose it’s probably a close enough approximation.
Nice, thanks. So just multiply out how many cubic feet the room is, then multiply that on a 1-10 scale based on how good the insulation is, then that is the number of BTUs you need?
However the problem is how many degrees can you make it colder or hotter with that calculation? A 1600 cu.ft. room with a 5000 BTU heater may sound good, but how many degrees will at 5000 BTU heater raise or a 5000 BTU AC lower the temperature?
This worksheet takes into account not only the size of the room, but also losses due to windows, insulation, exposure to the sun, and occupancy, and climate. It’s meant for air conditioners, but you can get a good first order approximation of how large a heater you’d need, as well.