Ok, here is my question.  How does keeping the temperature in your home lower your energy bill?  Here is why I ask.
~I got new windows in the spring. good, much better, insulation.  but keeping my temperature low has never been a strong point of mine; I like being able to be comfortable almost naked (if not so) in my house always.
~ So, assuming that there are no random energy leaks in a house (such as doors left open to the outside for hours, or wind gusts inside some how) the energy loss in the house should remain constant; for example, say 1 degree an hour.
~So, with the previous assumption unnegated, how does keeping the temperature lower help?  the energy used after, say, 2 hours of operation (a drop of 2 degrees) should be the same whether its from 68-70  or if it is 76-78.  the only difference would be if you have a regulating thermostat that drops the temperature when you are not there, in which case the energy expended would be more to raise the temperature back up.  if its simple caloric calculations (I have radiant heat, so it literally is the energy to raise a given amount of water by a given amount of heat)  then what am I missing when I hear that I should keep the temperature lower in the winter?! Why is this not making sense to me, someone help me out here!

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Your house temperature will not drop inexorably to absolute zero, rather it will tend toward the external temperature at a speed that diminishes as the difference between inside and outside approaches zero - equilibrium.

The nearer you are prepared to keep the internal temperature to the external temperature, then the smaller and slower will be the heat transfer through your walls, windows, roof and floor. In the limit, if your house was the same temperature inside and out then your heating bill would be zero.

Obviously this works in both directions, you might want your house hotter than the outside in the winter and colder than outside in the summer.

Clearly you don't want to do this so your cheapest bet is to insulate (as you have done) and slow the rate heat transfers though your walls.

If you had perfect insulation then once you'd got your house to the right temperature then you could turn of your heating/AC forever.

A little rambling - but does that help?
You bunch of egg heads! I was all muddled reading this... the replies gave me that "ah ha" moment. Ugh... I need caffeine!
Give a man fire and he'll be warm all night.

Set a man on fire and he'll be warm for the rest of his life.
it's the bulbs
Hi, I think this has been answered pretty well but a few thoughts that may help. Keep in mind that thermal energy is not equal to temperature. The amount of energy needed to change the temperature of a system by 1 degree c is the Heat capacity of the system. energy added = Heat Capacity * delta temp or
dQ = C * dt . Now back to your house. The heat flow out of you house depends on the difference in temp between the inside and outside ( T in - T out) call it DT. This is the thermal potential think of it like a Voltage in a simple dc circuit ( if that helps ) , now of course it also depends on how easy it is for the heat to flow or the thermal resistance ( how good your windows are) So now the Heat Loss form your house can be modeled as dQ/dtime = ( T in - Tout ) / R where R is the total thermal resistance between the inside and outside of your house. So this is just another way of saying that Watts of power lost by your house to the environment is directly proportional to the temperature difference and inversely proportional to how well insulated it is.
But since the title of your post was help with critical thinking don't take my word for it think about how you would do an experiment to test it.
So your question is if out side temp is constant 32, is the heat flow rate from inside to outside greater if the inside temp is 100 then it is if the inside temp is 75. Id say yes. If you heat your house up to 100 f when its a constant 32 outside then turn off the heat and time how long it takes to drop to 75 then time how long it takes to drop to 50 you will get a significantly longer time for the second.
in fact the time to drop the last degree from 33 to 32 would be very long. This does require solving a differential equation to calculate the time, but if you take the case where both inside and outside temps are constant its pretty easy to calculate the steady state energy flow from inside to outside (assuming we know the thermal resistance which of course we dont). And since energy is conserved to keep the inside temp constant that's how much heat / per unit time your furnace must be generating (average power).

Is there a cap where the heat flow saturates and increasing the internal temp does not lead to a higher rate of loss. I don't think so for any practical case. We could imagine some hypothetical material whose thermal resistance increased with temperature, so your walls and or windows insulated better when it was hot inside that would tend to flatten out the curve.

If you enjoy thinking about this you might want to take some physics or thermo dynamics courses.
Take Care
I think you can keep it at 76 and use less energy then most others do at 72 if you have really good insulation.
The rate of heat loss is a linear function of the temperature difference between inside and outside. Your improved windows and insulated walls still lose heat to the cold outside ambient. Insukation slows that rate of heat loss but does not stop it - if it did you would not need a heater inside since the heat you have would remain there. So, if it's 40 F out side and 70F inside you have a temperature difference of 30F, if it was 72F inside the difference would be 32F. A 32F difference is would lose about 6.5% more heat (30/32).

There is no god to decide that you've been a good person because you bought new windows and relieve you from the dictates of thermodynamics.

Here are the laws of thermodynamics, somewhat paraphrased for convenience:

1) You can never win, at best you can break even

2) It is only possible to break even at absolute zero.

3) You can not reach absolute zero

Corollary: You will lose.



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