Calculate the R -value of (a) a window made of a single pan e of flat glass (1)/(8) in. thick an

step 1 Today we're going to calculate the R values of some windows. First, recall that the R value is d

Calculate the R -value of (a) a window made of a single pan...

Key Concepts

Air Gap Insulation

Air gaps, when properly sealed and maintained, can act as effective thermal insulators because air has a low thermal conductivity compared to solid materials. The presence of an air space in a composite system can significantly reduce the overall rate of heat transfer. However, the performance of an air gap also depends on factors such as the gap width, temperature difference, and whether convection currents are present within the gap.

Composite Systems in Thermal Analysis

Many real-world materials, such as windows or insulated walls, are composed of multiple layers with different thermal properties. In these cases, the overall thermal resistance is determined by the sum of the individual resistances of each layer, arranged in series. This approach simplifies the analysis of complex structures by treating them as a combination of simpler, uniform layers.

Thermal Resistance (R-value)

Thermal resistance, commonly referred to as the R-value, is a measure of a material's ability to resist heat flow. It is the reciprocal of the heat transfer coefficient (U-value) and is used to quantify the insulating effectiveness of building materials and assemblies. A higher R-value means better insulation properties, indicating that less heat will pass through the material under the same conditions.

Conduction Heat Transfer

Conduction is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules in a solid or between phases in contact. In problems involving the R-value of building materials, the calculation often involves Fourier’s law of conduction, where the material’s thermal conductivity, thickness, and temperature difference determine the rate of heat transfer.

Transcript

00:01 Today we're going to calculate the r values of some windows.

00:03 First, recall that the r value is defined as r equals the sum of the thickness of each individual slab, l sub i, over the formal conductivity of each slab, k -0 -0.

00:18 And that's the sum over i.

00:20 So if you just had one glass slab, for a window, that would just be, you know, the thickness of that glass over the formal conductivity of the glass.

00:30 If you had like a house with, you know, wood, brick, insulation, more brick or something, you would have four things to add up and you just add them one.

00:41 And the other thing to remember is, for whatever reason, the convention for our values is to have them in u .s.

00:49 Units.

00:49 Specifically, there are units of feet squared hours degrees fahrenheit over btes, british fermil, units.

01:02 So we're going to have to convert to that at some point.

01:04 So to start off, let's do that first example, where it's just a single pane of glass of thickness l sub g of one eighth inch, which we're going to need to get into feet.

01:16 So let's go ahead and divide that by 12 to be 196 of a foot.

01:25 And we'll just leave that as the most accurate representation for now.

01:31 And we can also go ahead and go look up our formal conductivity for glass from table 20 .3, which gives us that case of g is equal to 0 .8, and that's given to us in watts per meter degrees celsius.

01:50 So our next step is we need to get from watts per meter degrees celsius to british formal units over feet times degrees fahrenheit times hours because that's the kind of unit we would need to divide a length of feet to produce an r value of this dimensionality.

02:18 So you can calculate it yourself or you can look it up or you can just trust me that the that one watt per meter degree celsius is equal to 0 .5.

02:36 This is a very rough approximates, i'm going to throw out a bunch of digits.

02:40 It's 0 .5781759 -9 -824 btus per foot degree fahrenheit hours.

02:55 And that's a long number.

03:00 So from now on, we're going to just define this as ru going forward.

03:09 So let's go ahead and calculate the r value for our single glass pane window.

03:16 So r sub g, r sub one glass equals the length of the glass over the thermal conductivity of the glass, which we've established is 1 eighth times 112 feet over 0 .8 watts per meters degrees celsius and our handy conversion coefficient of u.

03:48 And you can go ahead and calculate that out to equal 0 .0 .225.

03:57 And it is correctly in feet squared hours degrees fahrenheit per btu.

04:04 So that is the r value of just our single one eighth inch thickness class.

04:12 So let's look at a more formal window, specifically a window that has two layers of our quarter inch glass with a, sorry, eighth inch glass with a quarter inch gap of error between them...

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