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Old 02-01-2019, 01:55 PM   #1
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hypothetical furnace question


As the title states this is hypothetical and I am curious what the answer is because I don't know.

suppose you had 2 houses identical in every way
Its cold outside....say -5F

One house sets the thermostat at a constant 67
The other at a constant 75.
Once both houses are at the desired temperature does the 75 degree furnace run more than the 68 degree furnace to maintain their desired temperature?

If so what is the physics behind it? Why does the 75 degree house lose heat faster?
I'm not a physics guy or an HVAC guy and I can't wrap my head around the logical answer.
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Old 02-01-2019, 02:05 PM   #2
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Re: hypothetical furnace question


Assuming both houses have the same size and type of furnace, the one in the house set to the higher temp will run more to maintain.

Heat transfer is proportional to the temperature difference between inside and outside, all other things being equal. The role of the heating system is to replace the heat that's lost.

It's as if you have a bucket full of water with a hole at the bottom and you have to turn a tap on and off to maintain the correct water level. If you increase the water level, there's more pressure at the bottom of the bucket so it leaks faster and you have to have the tap on for longer periods of time to maintain the level.
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Old 02-01-2019, 02:18 PM   #3
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Re: hypothetical furnace question


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Originally Posted by user_12345a View Post
Heat transfer is proportional to the temperature difference between inside and outside, all other things being equal. .

That is what I was looking for. Does that have something to do with the 1st or 2nd law of thermodynamics?
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Old 02-01-2019, 02:23 PM   #4
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Re: hypothetical furnace question


Heat transfer is linear. For every 1 degree of temp difference X BTU of heat is lost or gained.


In your scenario, at -5F, if the 68F house requires 60,000 BTUs of heat to keep it at 68, then its losing a rounded 857 BTUs an hour per 1 degree of temp difference between the outside and inside.


The 75F house is losing 962 BTUs an hour per degree of temp difference between indoor and outdoor temp.


So the 75 degree home's furnace runs more often, and longer. And at -5F outdoor temp would need 66,856 BTUs an hour.
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Old 02-01-2019, 02:26 PM   #5
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Re: hypothetical furnace question


Temperature is the intensity of heat.

Heat is molecules of a substance moving around/vibrating and the higher the temperature, the more they move around/vibrate. You get more conductive and radiant heat transfer with more movement/vibration.

For convection, the hotter the fluid is, the lower the density, so the greater the temp differences is between fluids, the more the hot fluid gets displaced by cold fluid.

In a house you have cold, dense air leaking into low areas and hot air leaking out of high areas, ie attic ceiling. Initially, it starts with cold air displacing and pushing the warm air up, but once this process gets going you get a stack effect with warm air rising up, leaking out and cold air being pulled in. (technically, there's no suction -> just area of low pressure caused by warm air rising up and cold air of higher pressure from outside rushes in to replace it and equalize pressure)

Quote:
That is what I was looking for. Does that have something to do with the 1st or 2nd law of thermodynamics?


High density energy moves to area of lower density?

third law -> https://en.wikipedia.org/wiki/Third_...thermodynamics
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Old 02-01-2019, 02:29 PM   #6
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Re: hypothetical furnace question


I assumed the 75 would run longer I just had no clue why. I appreciate the time you guys took to pass on your knowledge.
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Old 02-01-2019, 02:34 PM   #7
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Re: hypothetical furnace question


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Originally Posted by craig11152 View Post
That is what I was looking for. Does that have something to do with the 1st or 2nd law of thermodynamics?

No its just heat transfer science.


There are three modes of heat transfer--- conduction, convection, and radiation. What has been discussed on this thread is conduction heat transfer. There will also be some effects by convection and radiation. Its actually a very complex science, but to say that if the temperature difference between inside and outside goes up by 10%, the energy lost will go up by 10%, is a reasonable approximation. Unless you are NASA.
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