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Stone Walls and Room Temperature

06/12/2009 3:00 PM

Hello,

I have a room in an old farm, and I would like to find which will be the temperature inside when outside will be -18 grade Celsius.

All the walls are exterior walls, the walls are made of stone, and lets say that its have the value R1 (meter^2xKelvin/Watt).And the floor has the value R2(meter^2xKelvin/Watt), and the roof has the value R3(meter^2xKelvin/Watt).

How can i calculate which will be the temperature inside of the building-room ?

Thank You.

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#1

Re: Room temperature

06/12/2009 3:06 PM

NOT A CIVIL ENGINEER in any way that could be interpreted

BUT the problem I had when trying to get this right was difficulty with the fact that while the stone has only an R1, there is no accommodation for what solar guys refer to as re-radiation.

But while I had adobe (mud brick) walls, which should only have an R1, in fact the building held temperature better than R1 walls should have, and the re-radiation effect "flattened" the swings in temp. that the R1 calculations indicated should be there.

Good luck!

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#2
In reply to #1

Re: Room temperature

06/12/2009 4:08 PM

...in fact the building held temperature better than R1 walls should have, and the re-radiation effect "flattened" the swings in temp. that the R1 calculations indicated should be there.

That comment reveals an ambiguity in the question. If the air outside stays at 18F and if other sources of heat like the sun or interior inhabitants stay constant, then the building will eventually reach some equilibrium temperature somewhat above 18F (because the sun is heating the building more than it is heating the air.)

But neither the air temperature or the sun are constant. The sun rises, travels in an arc across the sky, and sets. So the temperature inside will swing up and down around an average temperature daily, even if the air temperature is constant. Those swings might be large or small: if the building is massive enough, it might not swing at all. A cave could be considered a really really massive building, and temperatures deep inside a cave hardly change.

But it is impossible to tell how big those swings will be, or what will be the average value, from the facts given. If the building has a long side facing south, its temperature will swing up more during the day, and also probably be higher on average. If the building is subjected to strong wind all the time, then it will be cooler on average, because more heat will be carried away by direct conduction. Etc.

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#3
In reply to #2

Re: Room temperature

06/12/2009 4:32 PM

A cave could be considered a really really massive building, and temperatures deep inside a cave hardly change.

Agreed, but the "top level" calculations I was working with (since it isn't my field and was trying to teach myself out of an Audel's Guide to HVAC) only give you the option of Rock/Masonry wall = R1. (And as an aside didn't actually let me calculate ?insolation? either...seriously flawed) so south rooms and north rooms came out the same.

Which I think may be part of the problem this poster is running into.

Which led to calculations that showed triple digit BTUs per room on a windy winter night. And we just didn't have experiences that mirrored that. So really glad you came by!

How DO we calculate the heat needed for our "cave" f'rinstance?

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#5
In reply to #3

Re: Room temperature

06/12/2009 9:30 PM

I am pretty tired, so my thoughts aren't as organized as I'd want, but here they are.

Agreed, but the "top level" calculations I was working with (since it isn't my field and was trying to teach myself out of an Audel's Guide to HVAC) only give you the option of Rock/Masonry wall = R1. (And as an aside didn't actually let me calculate ?insolation? either...seriously flawed) so south rooms and north rooms came out the same.

Which I think may be part of the problem this poster is running into.

That is what I am saying. R values have nothing to do with temperatures, taken alone.

First of all, R is not a property of a material: rock does not have an R value of 1. R is a property of a structure or wall. Rock has an R value of 1 per inch of thickness. So a 10 inch thick wall of rock has a total R value of 10. That is why a thick fiberglass batt might have an R value of 20 while a thin one might have an R of 10, even though they are both made of the same material.

Second, insulation doesn't determine temperature. It only determines how quickly heat can flow through a material. If I put something wrapped in insulation with R 20, and another something with no insulation into my freezer, eventually both of them will be the same temperature. The one without insulation will just get there faster.

So even a very well insulated house, if left in constant conditions (and without a source of heat or cold inside) would eventually become the same temperature as outdoors.

But outdoors is not a constant condition. It swings between day and night. So at night, when it gets colder outside, the house begins to get colder inside, but very slowly. If it is well insulated, that cooling might be so slow that it is imperceptible.

(The thing that you mention about your thick rock walls absorbing heat and then re-radiating it at night, has to do with a different property of structures, and that is heat capacity. Your massive walls were able to store a significant amount of heat long enough to reradiate it at night. Nothing to do with insulation.)

(There is more to it, like the difference between heat and temperature, but maybe I'll think about that later.)

So the question the OP asks, what the interior temperature will be is impossible to solve if all you know is R values (as you discovered.) We have no knowledge of any of the myriad factors that play into interior temperature, such as how much sun is striking the house, what the prevailing winds are, whether the house is white or black, etc.

How DO we calculate the heat needed for our "cave" f'rinstance?

It cannot be calculated. It can only be measured empirically. If there is lots of heat entering the cave from below, either in the form of hot air or of heat being conducted through the rock, the cave might be very hot inside.

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#9
In reply to #5

Re: Room temperature

06/13/2009 7:11 AM

GA from me.

Everything I would have written, but with none of the "Cuss" words that I may have added....

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#11
In reply to #5

Re: Room temperature

06/13/2009 9:26 AM

Wish I'd asked before I bought the manual - I'M understanding much better now - hope the OP is too.

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#20
In reply to #2

Re: Room temperature

06/13/2009 9:28 PM

Hello karlc,

Please allow me to point out that, the OP said 18 ͦͦ Celsius.''''''

Take care

bb

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#28
In reply to #20

Re: Room temperature

06/15/2009 4:04 PM

the exterior temperature it is minus 18 grade Celsius

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#4

Re: Stone Walls and Room Temperature

06/12/2009 5:53 PM

It depends on heat source you have inside. Δθ = R*P/S, P in watt S in m² this is valid for all surfaces since temperatures in and outside are same for all.

Σ P= Δθ*Σ (S/R) = Ptot thus Δθ= Ptot/Σ(S/R). Tin=Tout+Δθ

In your computations do not forget the windows and doors since they have different thermal losses.

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#29
In reply to #4

Re: Stone Walls and Room Temperature

06/15/2009 4:11 PM

there isn't any heat source inside, and there won't be one.

after I will calculate the interior temperature (when outside are minus 18 grade Celsius) I will calculate the thermal resistence, that named R1, for an isolated wall because I will need to be inside around 2 celsius degree (when outside are minus 18 grade Celsius).

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#32
In reply to #29

Re: Stone Walls and Room Temperature

06/15/2009 4:42 PM

I somehow have the feeling that you have not understood many of the (good) posts already received....

No matter how much insulation you use, without a source of heat inside, the room will cool down till it is the same temperature as outside.

The insulation will slow this process down, but it canot stop it!!!

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#35
In reply to #32

Re: Stone Walls and Room Temperature

06/16/2009 11:21 AM

i understand the most, maybe all the posts. the problem it was that i've tried to find a way for that calculation. and i've thought that there it is a thing about heating transfer which i don't know and it can help me.

i wanted to talk with a proffesor or with somebody wich really knows thermodinamics.

thank you for answer me.

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#36
In reply to #35

Re: Stone Walls and Room Temperature

06/16/2009 11:55 AM

Believe me, you have all the information already. Without a heat source, the room will get colder and colder till it is at the outside temperature.

Insulation slows things down, nothing more nothing less.....

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#37
In reply to #35

Re: Stone Walls and Room Temperature

06/21/2009 2:59 PM

To me1234, some of the the replies you have received are what physics professors (or people who "really know thermodinamics" [sic]) would say. Others, though they don't exactly answer your question, are what experienced engineers and builders would say. Sorry to say it, but you don't understand enough physics to even ask an answerable question. The others have pointed out the flaw in your question, repeatedly.

To the others, there is a possible heat source in the house, and that is a human being, which gives off about 100 watts of heat, IIRC. You could assume there is one human being in the house for maybe 14 hours a day.

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#38
In reply to #37

Re: Stone Walls and Room Temperature

06/21/2009 5:04 PM

Well put, but unless that "human body" is there naked, you will not get much heat from it in the room, it will be too well insulated clothed!!

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#39
In reply to #38

Re: Stone Walls and Room Temperature

06/28/2009 1:19 AM

(sigh) As I and others have pointed out repeatedly, insulation doesn't affect what the temperature will be ultimately, it only affects how long it will take to reach that temperature. True, if the occupant is absent for half the time, there might not be enough time for the occupant to provide much heat. Or the occupant might provide a significant amount of heat, even when clothed. You would have to the calculations to find out!

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#6

Re: Stone Walls and Room Temperature

06/13/2009 1:06 AM

Guest,

There are a a couple assumptions behind the ASHRAE Fundamentals tables of R-values and how they are usually used in calculating heat gain/loss in structures. The biggest one is that the structure is made of light-weight materials (very little thermal mass). The related second one is that heat transfer across the insulating barriers is instantaneous, at the rate allowed by that barrier's R-value. When you are dealing with a mass wall, such as the stone in your question, the wall will act as a source or sink for heat. Among the solar people, there is a "rule of thumb" that says that in a solid masonry wall, the heat transfer across the wall is delayed by one hour for each inch of thickness.

Now, your question didn't state the thickness of the wall. Nor did you indicate whether or not we are to consider other variables such as solar gain, insolation, and internal gain from the presence of workers or machines. If all these variables are kept constant (certainly not a real-world condition), then eventually the room temperature will reach a constant value as determined or allowed by the calculated amounts of heat lost through the floor, walls, and ceiling of the structure.

Does this help? --JMM

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#7
In reply to #6

Re: Stone Walls and Room Temperature

06/13/2009 1:22 AM

See? That's what I said!

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#30
In reply to #6

Re: Stone Walls and Room Temperature

06/15/2009 4:16 PM

I will kept for the calculations, the variables constant.

So how can I calculate the room temperature ? Because I don't know...

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#33
In reply to #30

Re: Stone Walls and Room Temperature

06/15/2009 4:45 PM

See my last post.

The temperature will continue falling (with no heat source) till it reaches the outside temperature. The rate will slow the nearer it gets to the outside temperature, but it will not stop, unless you have a heat source....

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#8

Re: Stone Walls and Room Temperature

06/13/2009 6:23 AM

I have not the intention to make course of heat transfer but I read the different comments and noticed that there are misunderstandings which should be cleared:

- at a wall between two fluids (in this case air on both sides) there are 3 zones of heat transfer: via convection at the out and inside between fluid and wall characterized by a coefficient of resistance Rconv having the units °K*m²/Watt which means that the resistance to heat flow measured in temperature difference is higher when area is smaller and when more power is passed through

- in the wall by conduction every material being characterized by its thermal conductibility λ in Watt/(°K*m). The resistance of a 1m² of the wall will be Rwall and can be computed as Rwall=t/λ and has same units °K*m²/watt.

In these later value the wall thickness is already considered. This is usual in civil engineering where walls are more or less standardised as thickness.

Those 3 resistances are in series and can be summed Rtotal= Rconv out+Rwall+Rconv in. If it is possible to consider Rconv in as almost constant Rconv out depends on several factors as for instance wind intensity.

Those values are for a steady-state condition which means that the temperature field does not change over time.

In reality conditions change continuously either due to day solar energy or to wind.

This means that we are confronted to transient situations which make that for instance the internal room temperature will be variable for same input of thermal power for heating. In this case two factors play a role one is the Rtotal value it self and the other is the thermal inertia of the walls and of the air in the room. The play of the 2 leads to a time constant which determines how changes of one of the variables (power input, out side temperature) will affect internal temperature. For instance the given example of a cave, if the depth of the cave if over a value i.e. the soil mass between outside temperature and cave has an inertia big enough the time constant is such that the 24 hours cycle is almost totally filtered and the inside temperature (cave) is almost constant (good for wine). There is in fact an optimal cave depth which considers as well the surface variations as the geothermal degree of roughly 1°C/30m depth.

The faster or slower cooling/heating of a box depends also of the 2 factors. It should be noticed that Rtotal is for a surface unit and the thermal inertia depends on volume and mass so that a spherical box will be better than a cubic one since for same volume its transfer area is smaller.

Now in some comments there was a misunderstanding between R in °K*m²/w and the inverse of heat conductivity in °K*m/w. I hope I could help for a better understanding.

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#21
In reply to #8

Re: Stone Walls and Room Temperature

06/13/2009 9:57 PM

I found the posts by nick name extremely helpful. To try to further clarify some nomenclature, I will add the following. k = thermal conductivity [W/(m·K)]; C = thermal conductance [W/(m2·K)], sometimes called heat transfer coefficient (h); R = thermal insulance (m2·K/W) = 1/C. By definition, C = k/L, where L = length of material in direction of heat transfer (in this case, wall thickness). Therefore, substituting and/or rearranging, we have k = L·C, and R = L/k.

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#10

Re: Stone Walls and Room Temperature

06/13/2009 7:39 AM

It`s a little bit like asking:

"My mains voltage is 230V AC and my cable is 10 m long. How much current does my toaster draw ?"

You have to assume an amount of energy from your radiator inside in order to answer that question. If you dont spend this amount of energy then you have only to wait long enough and your temperature inside will (with a rough simplification) always be the same as the temperature outside - because, where else should come the difference from ?

When you switch of your refrigerator the inside temp will also become the outside temp.

Regards Uwe

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#12

Re: Stone Walls and Room Temperature

06/13/2009 10:33 AM

Its going to be cold, I should imagine that sleeping in 32°F or 22°F or whatever is not going to be much fun.

If the outside of the house is unattractive and you like the look of the stones from the inside, insulate the roof and the whole outside of the house. It will take longer to warm up, but at night when the fire goes down, you will find that the temp goed down real slow as the walls give up their stored heat. Thats how I like it.....

If you want the outside to remain as it is, insulate the inside, but from then on, your rooms will be slightly smaller and hanging stuff on the walls in some cases almost impossible - cupboards and pictures. But it will warm up quicker with a fire going..... also cool down quicker....

Take your choice.....

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#13
In reply to #12

Re: Stone Walls and Room Temperature

06/13/2009 11:23 AM

Isolating from the inside has to be planned well - an often observed error occurs when the dew point suddenly lies inside the wall and leads to condense moisture then.

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#14
In reply to #13

Re: Stone Walls and Room Temperature

06/13/2009 11:43 AM

Correct but there are special plastic sheets that need to be sealed together to prevent any breathed out moist air getting to the cold walls.....something that many (most?) forget to do....even professionals!!!

I sealed up a room some years ago and had to tell the professional to shutup and use the sheets as I was paying, not him!!!! In places we had 10" of fiberglass insulation (uneven walls.....)

We have had zero problems......our heating costs went down dramatically......but I only hang pictures on those walls, nothing more......

Recently we insulated the whole house on the outside, much easier and I feel much netter.....you live and learn.....

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#15
In reply to #14

Re: Stone Walls and Room Temperature

06/13/2009 11:59 AM

Agreed with both of you

I was looking at how/where to insulate and seal and ran into a study on masonry wall retrofits (I believe former factory spaces) that explicitly discussed considerations on moisture.

Traditional adobe and stucco "breathes" and I was considering a solution that didn't, so pondered carefully, and decided to use a barrier to keep the "wall" dry.

And after much consideration, like you Andy, I decided if ever (project currently on hold) I would rather insulate outside and add more stucco to finish.

Since the construction was circa 1970, while I then wanted to control interior moisture with an air-to-air heat exchanger, practically I would have to use a typical bath-to-exterior fan initially.

With all this longwindedness, I would end up storing heat, but in a dry wall.

But this house has areas where a pencil can be inserted around doors, and cheap (although double-pane) windows, so the significance of air-to-air vs outlet fan will be a while and a lot more work, before it gets "out of the grass."

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#17
In reply to #15

Re: Stone Walls and Room Temperature

06/13/2009 3:05 PM

I might have written your post, the cellar had more air movement than outside on windy days before, but not anymore!!!!

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#16
In reply to #12

Re: Stone Walls and Room Temperature

06/13/2009 12:15 PM

"But it will warm up quicker with a fire going..... also cool down quicker...."

If insulation is increased it works as well for heating as for cooling the same, then why the difference? It warms quicker because less energy is lost to outside, since less energy is lost per time unit then it will cool SLOWER. Or am I wrong?

The energy balance equation is: accumulated energy = generated energy - lost energy

Accumulated energy = M*cp* dT M= mass inside kg, cp =specific heat (mean value) in J/kg; T inside temperature °K or °C

Lost energy = (T-Tout)*A/R *dt A= heat transfer area (walls, windows, aso) R= averaged thermal resistance °K*m²/w dt= element of time

Generated energy= H( watt)*dt

For Tout= constant (approximation) dT= d(T-Tout)

Equation becomes: M*cp*d(T-Tout)= dt*(H-A/R*(T-Tout)) it is a differential equation which leads to an exponential solution with a time constant τ=(R*M*cp)/A

If H>0 then there is a heating and if H=0 the temperature will drop but in both cases the time constant is the same. Or am I wrong?

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#18
In reply to #16

Re: Stone Walls and Room Temperature

06/13/2009 3:09 PM

With outside insulation, the stone walls take a lot of heat at first and store it. When the fire goes out overnight, this heat, because the outside is well insulated, can only leach back into the room...which is really nice.

When insulating on the inside, you do not have any sort of storage block, so it warms up and cools down quicker, but of course still much better economically than without insulation!! Usually, unwanted drafts have also been cut down on to assist further.....

I did not make myself clear at all before......sorry.

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#19
In reply to #18

Re: Stone Walls and Room Temperature

06/13/2009 3:17 PM

Clear enough, I thought

Of course this is the house with only 1" of foam and a lot of tar on the roof. Which IS the shell.

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#22
In reply to #18

Re: Stone Walls and Room Temperature

06/14/2009 8:24 AM

It is ok my comment was only in order to see if there was an analysis or only a "say so".

Of course with out side insulation the internal mass increases and the time constant as well. So that the time to reach a higher temperature inside increases too since not only the air has to we warmed but also the walls.

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#23
In reply to #22

Re: Stone Walls and Room Temperature

06/14/2009 9:13 AM

Its really onlly a "say so" but anyone with minor knowledge of physics will "cotton on" quickly I feel.....

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#31
In reply to #12

Re: Stone Walls and Room Temperature

06/15/2009 4:22 PM

if I will isolate the inside there will be a problem: the condens.

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#34
In reply to #31

Re: Stone Walls and Room Temperature

06/15/2009 4:46 PM

Only if you do it wrongly!!

As with all jobs, there is a correct way and a large number of incorrect ways.....take your pick!!

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#24

Re: Stone Walls and Room Temperature

06/14/2009 2:16 PM

is it because I lack any formal high and technical education ,that I wonder why no one is mentioning the the question for the relation between the walls area and the inner volume?

As much as I know,the square/cube rate playes an important role in any thermodynamic calculations.

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#25
In reply to #24

Re: Stone Walls and Room Temperature

06/14/2009 2:32 PM

Hello az native,

Thats a fair remark. But it sounds as if the building has been built already, and is just awaiting the stucco?

bb

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#26
In reply to #24

Re: Stone Walls and Room Temperature

06/14/2009 7:33 PM

Mentioned in #8

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#27
In reply to #26

Re: Stone Walls and Room Temperature

06/14/2009 8:29 PM

Hello nick,

sorry for the duplication.

Take care......

bb

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Take care, bb ----- >> "HEAR & you FORGET <-> SEE & you REMEMBER <-> DO & you UNDERSTAND" << =$=|O|=$= >> "Common Sense is Genius dressed in its Working Clothes" << <> [Ralph Waldo Emerson]
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