My house is heated with radiators, and my furnace is a “hot tank” system, meaning that the furnace cycles on and off to keep the water in the tank at a constant temperature, and the thermostat simply controls the pump the circulates the hot water. One of the side effects of this type of system is that it needs to be shut off when not in use; if I left it running all summer it would eat up all of my heating oil keeping the tank warm while never actually heating my house at all. So my question is this: is there any length of time for which it is inefficient to shut the furnace off? If I turn it off for, say, a month, the water in the tank will cool, and need reheating when the system comes back on. But that will only take half and hour or so, while if the system had stayed on during that time it would have consumed considearbly more energy maintaining the tank temperature. Does this continue to be true for shorter and shorter time slices?
I think your energy savings would be proportional to how much you lowered the tank temperature multiplied by how long you lowered it for.
You will note that while the temperature is going down it is at infinitely many different “lowerings” but for infinitely little time each. So what you really want is the integral of the temperature drop over time.
Note that your tank loses heat to the rest of the house, if it’s indoors. So, if there is any value in having that heat in your house, that value offsets the savings.
Strictly speaking, you’ll always lose energy when the water is warm, and you’ll lose energy faster from convection if the difference in the tank temperature and the air around the tank is greater (Newton’s Law of Cooling). Furthermore, you’ll lose energy faster from thermal radiation if the temperature of the tank is hotter, too. You can’t perfectly insulate the tank, so you’ll always be dealing with these losses, until the temperature of the tank is the same as the temperature of the air.
So, it’s always better to turn off the heat source if your goal is to save money (i.e., you don’t get any benefit by “keeping it warm,” even for short time periods. That is, unless it takes a significant amount of energy to start the heater). If your goal is to have hot water in a reasonable amount of time, then you can turn it down but not off, until you are satisfied that you’re saving enough money and getting up to an acceptable temperature in a short enough time.
Incidentally, the same argument holds true for using an air conditioner – if you want to save money, turn it off when you leave (and not simply down a bit). Upon your return, you’ll have to deal with being warm in your house until it cools down, but you’ll save more money in electricity costs.
Nitpick:
Furnace = forced air
Boiler = hot water/steam
