True?: Heat rises, so you can put thermostat lower upstairs

[pandaexpress]

My friend said he places his thermostat lower upstairs, because heat rises and he says that the heat from downstairs will naturally heat your upstairs. Doing this would save money on your electric bill he said.

I had a debate with him about this. I actually figured that it would be the reverse. Here was my logic...I felt that if heat was rising from downstairs, then that would mean that it was escaping and that you'd need MORE heat pumped out to heat the downstairs and that would increase your electric bill.

Any thoughts from you physics heads? :)

 

[NascentOxygen]

Upstairs can be warmer. For starters, it has a warmed floor! It's well-insulated from the cold ground, and above the layer of cold air that hugs the ground on cold mornings. Lack of insulation in the ceiling may, in Winter, negate some of these advantages.

When I lived in a third-floor apartment I discovered that after I'd left a book on the floor overnight the carpet underneath it would be noticeably warm. Thanks to the heating in the apartments below, I was able to economize on Winter heating. :)

 

[Lok]

My friend said he places his thermostat lower upstairs, because heat rises and he says that the heat from downstairs will naturally heat your upstairs. Doing this would save money on your electric bill he said.

I had a debate with him about this. I actually figured that it would be the reverse. Here was my logic...I felt that if heat was rising from downstairs, then that would mean that it was escaping and that you'd need MORE heat pumped out to heat the downstairs and that would increase your electric bill.

Any thoughts from you physics heads? :)

Heat does go up in a house mainly through the staircase. And this would mean that if all heating elements are of equal power, then the top floor would be warmer.
As nascentO2 pointed above there are many factors that can influence this, one more being a staircase door or curtain (not usual).

Placing the thermostat lower will mean it senses a lower temperature and thus heat the house more. This is not economical at all, it is just like setting a higher temperature on the thermostat itself. For true economy, set your heating elements for more radiative power downstairs to compensate for the updraft, by using a thermometer in both floors and comparing. Basically uniforming temperature is both comfortable and more efficient as in a well isolated house.

Edit: I forgot to mention that, the reason why a uniform temperature is better than a gradient. Basically the two hot/cold non-uniform parts add to more energy being radiated away as emissive power is not linearly dependent on temperatue, rather T⁴, so the hot part loses a lot more energy than the cold part would save, compared to a uniform mean.

 

[russ_watters]

Edit: I forgot to mention that, the reason why a uniform temperature is better than a gradient. Basically the two hot/cold non-uniform parts add to more energy being radiated away as emissive power is not linearly dependent on temperatue, rather T⁴, so the hot part loses a lot more energy than the cold part would save, compared to a uniform mean.

No, the vast majority of heat loss through a house is via convection, not radiation. It is a direct proportion to temperature difference.

More general advice than what has been given above: heat the room you are in and don't heat the rooms you aren't in. Any room that is colder loses less heat to the outside and therefore takes less energy to heat. I'm constantly adjusting the vents in my house to accomplish that. In addition, I like it cooler when I sleep, so I keep the vents in the master bedroom closed during the day so that it isn't too warm when it is time to go to bed.

And for the OP's question: if you have thermostats both upstairs and downstairs, you still set them for what you want the temperature to be. They are thermostats, they control to a specific temperature: so since heat rises, the upstairs thermostat just turns on the heat less often. You don't turn down the thermostat to achieve the same temeprature!

 

[sophiecentaur]

The simple answer to the OP is that the thermostat will keep itself at the required temperature. IF it is sited at the top of the house, then it will require less energy from the system to keep it at a given temperature. Downstairs will be cooler. If sited downstairs, the Upstairs will be warmer and you will need more total energy input.
You can have as complicated an answer as you want, beyond that basic one and you would need to specify what the actual situation is.

 

[Lok]

No, the vast majority of heat loss through a house is via convection, not radiation. It is a direct proportion to temperature difference.

True, it is small compared to convection and conduction, yet it is what makes the difference in the heat loss of a house with a temperature gradient vs. a house with a uniform mean temperature, given the same heating power input. For the big outer surface of a house it should not be negligible.

I was hasty in my statement, thank you for completing it.

 

[russ_watters]

True, it is small compared to convection and conduction, yet it is what makes the difference in the heat loss of a house with a temperature gradient vs. a house with a uniform mean temperature, given the same heating power input. For the big outer surface of a house it should not be negligible.

No, sorry, it really doesn't make the difference. Radiative loss is ignored in building heat loss calculations.

 

[Lok]

No, sorry, it really doesn't make the difference. Radiative loss is ignored in building heat loss calculations.

My calculated radiative loss for this winter is 15% of my whole heating bill. By using 0.5 for emissivity (as I cannot really know the emissivity of a brick concrete wall I cut the error in half) , a 2 degree Kelvin difference between outside temp and outside wall temp (both measured), and dividing by my heating bill for a month converted in W (so a mean). I know it is not used in heat loss calculation but I cannot call it negligible.
And this tells me I need to insulate my outside walls to reduce their overall outside temperature.

 

[CWatters]

Is the temperature of the outside wall 2k hotter than ambient due to losses from within the house or the sun heating the walls?

 

[CWatters]

As for the OP. I think Russ has the answer. Turning down the upstairs thermostat makes no difference IF the room is already above the set temperature because it's heated by another source (eg from downstairs).

 

[russ_watters]

My calculated radiative loss for this winter is 15% of my whole heating bill. By using 0.5 for emissivity (as I cannot really know the emissivity of a brick concrete wall I cut the error in half) , a 2 degree Kelvin difference between outside temp and outside wall temp (both measured), and dividing by my heating bill for a month converted in W (so a mean). I know it is not used in heat loss calculation but I cannot call it negligible.
And this tells me I need to insulate my outside walls to reduce their overall outside temperature.

Well there's a couple of problems:
1. 2k is probably too much -- under what conditions did you measure? Recognize, as said, that during the day you gain heat from the sun, and at a much faster rate than you lose heat at night from radiation. But more to the point:
2. You weren't explicit, but it sounds like you are under estimating the night-time radiation because when you radiate, you radiate into space, against a 3K black body, not against your 270k (or whatever) outside air. The difficult part is how much is radiated up vs how much is netural to the ground. It's probably best to model your house as a half-sphere or flat plate (the roof), pointed at the sky. But then, if your roof is elevated and insulated, you still have convection causing most of the actual heat loss between your house and the roof.
3. Was that 2k lower or higher? If your house is radiating, in order for that to be a factor, the surface temperature should be lower than ambient.
3. No matter what, the heat has to travel through the wall. So even if some of it radiates off the wall surface, it still has to conduct through the wall, and that's what allows or stops all heat loss.

Let's assume you meant the wall was 2k below ambient outside, on a 0C day, when it was 20C inside. That 2k difference is 10% of the temperature difference, or a 10% increase in heat loss. But again; only at night, on cloudless days.

Wall heat loss due to convection isn't terribly difficult to estimate if you know the construction and how much insulation it has. If your outside wall temperature is really 2K above ambient (and your inside wall 2k below ambient?), that implies really terrible insulation and huge convection/conduction heat loss.

 

[Lok]

Well there's a couple of problems:
1. 2k is probably too much -- under what conditions did you measure? Recognize, as said, that during the day you gain heat from the sun, and at a much faster rate than you lose heat at night from radiation. But more to the point:
2. You weren't explicit, but it sounds like you are under estimating the night-time radiation because when you radiate, you radiate into space, against a 3K black body, not against your 270k (or whatever) outside air. The difficult part is how much is radiated up vs how much is netural to the ground. It's probably best to model your house as a half-sphere or flat plate (the roof), pointed at the sky. But then, if your roof is elevated and insulated, you still have convection causing most of the actual heat loss between your house and the roof.
3. Was that 2k lower or higher? If your house is radiating, in order for that to be a factor, the surface temperature should be lower than ambient.
3. No matter what, the heat has to travel through the wall. So even if some of it radiates off the wall surface, it still has to conduct through the wall, and that's what allows or stops all heat loss.

Let's assume you meant the wall was 2k below ambient outside, on a 0C day, when it was 20C inside. That 2k difference is 10% of the temperature difference, or a 10% increase in heat loss. But again; only at night, on cloudless days.

Wall heat loss due to convection isn't terribly difficult to estimate if you know the construction and how much insulation it has. If your outside wall temperature is really 2K above ambient (and your inside wall 2k below ambient?), that implies really terrible insulation and huge convection/conduction heat loss.

1. Complete data: Area 56 m^2, emissivity 0.5 (0.8 would be closer from what I've found), Twall 273, Tambient 271 . Power loss 256W (not a lot), Monthly power consumption 1735.764 W.
2. measured the temperature at 22:00 after a really cloudy miserable day (w/o precipitation). Wall was straightforward measurement 0(+-0.1). Ambient was even easier, took a shot at the ground and night sky (cloudy). Both had that -2 Celsius (+-0.1). Measured with a cheap temperature laser gun (don't remember the maker).
3. It was winter so the wall is hotter than outside ambient, and my walls are completely uninsulated brick with a shot of concrete. I usually talk about outward heat loss, so from the house (apartment in my case) to outside ambient, as it is true loss, inside transfer is not a loss in my opinion, unless it affects outside loss. As such I really mean the outside surface of my house had 0 Celsius and the outside ambient had -2. While it should be the same on the inside the surface calculation + conductance through heat sinks is too much a bother.
I really doubt that you can sense a 3 Kelvin night-sky temperature considering we have 10 tonnes of atmosphere above us much hotter than space. When pointing at a clear sky it was colder than usual but only by a few degrees (remembrance).

Convection is easy to estimate for the inside but given varying wind makes it slightly complex for the outside. And while nobody bothers with radiative power+conductance+convection, I'm sure they still pump the convection value by a factor of 1.2 without knowing why (one of those constants).

 

[russ_watters]

Sorry for the very late reply:

Power loss 256W (not a lot), Monthly power consumption 1735.764 W.

Monthly should be in kWh, and those numbers don't jive. If you slipped a decimal and meant 173.6 kWh, that would be close.

Is electricity your sole source of heat? You're right, that isn't a lot, even for an apartment, with only a small outside wall exposure. I use about 450 kWh per month, and that only includes the fan that drives the heater, not the heat itself! I have a 150 sq m townhouse, with one shared wall. I live near Philadelphia, Pennsylvania, with an average winter temperature of about 0C.

It was winter so the wall is hotter than outside ambient, and my walls are completely uninsulated brick with a shot of concrete.

Ahh, that's starting to make some sense, for the temperature you are seeing. Yes, for uninsulated walls, the wall temperature can be above ambient. In an "ideal" case of very thin and absolutely no insulating value, the wall temperature would be exactly halfway between the inside and outside temperature. The better the insulation, the closer you get to the ideal, where the surface temperature is exactly equal to the air temperature (inside and outside).

An uninsulated concrete wall has an insulation value of about 0.176 k*m^2/W (US: R-1). In my area, codes require 2.3 (US: R-13) for new houses.

Now, given the size of the wall and temperature, the heat loss should be about 6300 W. So your numbers on required heating don't make any sense at all. You sure you aren't getting your heat for free?

I really doubt that you can sense a 3 Kelvin night-sky temperature considering we have 10 tonnes of atmosphere above us much hotter than space. When pointing at a clear sky it was colder than usual but only by a few degrees (remembrance).

Probably true -- and the atmosphere, even when dry, does absorb at least a little IR. Still, if radiation is the primary heat loss, it causes surfaces/objects to be colder than ambient, not warmer.

 

[Lok]

Monthly should be in kWh, and those numbers don't jive. If you slipped a decimal and meant 173.6 kWh, that would be close.

I like to transform everything to simple W or J (rarely). So 256 is in simple W. The 1736 W or monthly average heating power, came out of a close to 1.2 MWh that my gas bill shows of course divided by seconds (I did ignore the electric, as it contributes only lightly to the monthly average power). For some reason they decided for themselves to bill us according to gas quality in MWh/cub meter although they measure volume, just to add to the general confusion that is the gas bill and it's pricing.

Now, given the size of the wall and temperature, the heat loss should be about 6300 W. So your numbers on required heating don't make any sense at all. You sure you aren't getting your heat for free?

I don't know my R value, And I'm not sure how insulating the brick in the wall is ( it could be of Porotherm type which insulates better, but I just don't know). And I do share walls with lots of neighbors, but they are not this giving. I do agree something can be off as I have no values for wind or humidity.
Still my heater is 24 kW, yet at a 6.3 kW it should work at full for 8 hours per day (which it doesn't), my 1.7kW seems fine to how much it is in heating mode.

Btw had the chance to measure the nightsky a few nights ago, a chilling -38 C, when it was only -5 outside ambient, after a moderate snowstorm.

 

[russ_watters]

I like to transform everything to simple W or J (rarely). So 256 is in simple W. The 1736 W or monthly average heating power, came out of a close to 1.2 MWh that my gas bill shows of course divided by seconds (I did ignore the electric, as it contributes only lightly to the monthly average power).

Oh...sorry, you did some odd math there. A megawatthour is a million watts for an hour -- not watts for a second. So you divide by the number of hours in a month, not the number of seconds. So 1.2 MWh or 1200 kWh is 1.67 kW or 1667 Watts, average power draw. That makes a lot more sense. Not sure what the 256 W is supposed to be though...

For some reason they decided for themselves to bill us according to gas quality in MWh/cub meter although they measure volume, just to add to the general confusion that is the gas bill and it's pricing.

MWh/cub meter is the energy capacity of the fuel. So they measure the volume, then translate that into energy.

I don't know my R value, And I'm not sure how insulating the brick in the wall is ( it could be of Porotherm type which insulates better, but I just don't know). And I do share walls with lots of neighbors, but they are not this giving.

Well, even drywall or plaster with an air gap can double it from totally uninsulated concrete.

Still my heater is 24 kW, yet at a 6.3 kW it should work at full for 8 hours per day (which it doesn't), my 1.7kW seems fine to how much it is in heating mode.

Yes.

 

[jh0]

In my opinion radiatiative losses must be important, although surely smaller that convective losses. That's why temperatures drop considerably faster on clear nights compared to cloudy nights.

 

[Lok]

Oh...sorry, you did some odd math there.
Not sure what the 256 W is supposed to be though...

Odd indeed. While dividing by the hours would make a lot of sense. I first transformed into Joules the converted into W (which implies an unnecessary multiplication and subsequent division by 3600, yet i like to see both values in my excel table). The 256 W is the radiative power of a body of the given surface, emissivity and temperature difference, at least what i came up with.