Jambruins said:
I realize that is uses less total energy but is the total energy saved offset but the amount of energy used to get the temp back up? I think it is much easier to lose energy than it is to gain energy.
total energy is all of the energy expended over the day, it includes the ramp back up time.
The only reason you have to burn fuel is to replace lost energy, right? Otherwise when you got the house to 71 in November it would stay that way. We know that's not true - warmer bodies transfer their heat to cooler ones. In this case your house is the warm one and the outdoors is the cool one. How fast that happens depends on 2 things: the thermal properties of each body (what is your house made of, how well is it insulated, etc) and the temperature difference between the two objects. We burn fuel to replace the heat lost in that transfer and keep a steady temp inside.
newton's law of cooling applies to the second factor - the temperature difference between inside and outside. The law basically says that the rate of heat loss is proportional to the temp differential. If there is a 70 degree difference you may be losing 20KBTU of heat an hour, but when there is just a 50 degree difference you might loose just 15KBTU. The actual numbers are made up and depend on the construction of your house, but the principal is the same: the bigger the temperature gap the greater the RATE of heat loss. If you close the temp gap you lose heat slower and therefore have less total energy to replace when you turn the tstat back up than you would have slowly leaked out if you just left the tstat alone.
my example, if there is a 70 degree difference you are loosing 20KBTU an hour whether or not the stove is running. If the stove is running on medium or so you are essentially replacing those 20KBTU each hour and keeping it a steady temp inside. If however, the stove is off then the temperature inside begins to drop. Maybe you loose 20KBTU the first hour, but the second hour it is cooler inside (meaning a smaller differential between inside and outside) so you lose something less - maybe 18KBTU, the third hour it is cooler still - maybe 15KBTU.. let's say this is as cold as you want it to get so it stays at that temp for 2 more hours - losing another 15KBTU each hour which the stove replaces by burning on low keeping the inside temp steady and cool.
OK, so now its cool inside, and you've burned 30KBTU worth of pellets in the last 2 hours to keep it at the minimal temp. How much energy do you need to get back to the original toasty room temp? It's exactly how much energy you have lost - remember all we ever do is replace lost heat. That would be 20 + 18 + 15 = 53 KBTU. Add the 30KBTU the stove burned on low and you're back at room temp having spent 83KBTU.
If you had stayed at room temp the whole 5 hours, losing 20KBTU an hour, you would have used 100KBTU worth of energy. In each case the room is the same temp afterwards and all energy is accounted for. Your house is just more efficient at holding onto the heat it already has when the differential between inside and outside is less.
(again, the actual BTU rates are totally fabricated and depend on your house and the actual temperature differential, but the priniciple is right.)
