 Okay, the last topic that we're going to talk about in relation to the idea of thermal resistances relates to our values and if you go to any hardware store and you're going to buy insulation for your house, you'll find that they always talk about our values in terms of the different types of insulation that you can buy. Consequently what we want to do is we want to be able to relate that to what we're looking at in this course. So the our values begin, they are related to thermal resistance, but there's a difference between British units and SI and that's what we'll elaborate on in this lecture in this segment. So if you recall the equation that we've been using for thermal resistances is this one. Let's isolate for the thermal resistance. So essentially what the thermal resistance is is delta t divided by q. If we look at the units, that's degree C per watt. Now the r value, what it is quantifying is delta t divided by heat flux, so q per unit area. And so consequently the units of an r value are a little bit different from the thermal resistance in that what it will be is degrees C meters squared per watt. And so a way of thinking of the r value if we're looking at this in SI is it is essentially the temperature drop for 1 watt of heat flowing through 1 square meter squared of material, so 1 square meter in terms of the area. So what it quantifies, so you can see if you have 1 watt and 1 square meter, q over a is then going to be equal to 1. If you put 1 into this equation, then r value is equal to delta t. And that's how we get that relation. Now the r values that you find in hardware stores, however, those are not in SI. So we'll take a look at that. Before we do that, however, I'm just going to make a comment if you're dealing with pipes and the r values for pipes are given by this relationship. Okay, so that's the r value if you're dealing with a pipe. Now if you go to any hardware store, Home Depot, Lowe's, any of those, r values that are reported there, they're not in SI. And so we need to be able to convert that. And so if you go on, you take a look, you'll see things like r12, r16, r20. And the sum, assuming it's for walls, for attics, the number would be larger. But any of these, r12, r16, r20, any of those, those are done using the British thermal unit. And the conversion is that. So if we want to compute an r value in SI, we would have to multiply by 1 over 0.1761, which is 5.679. And that would equal the r value. And in non-technical lingo, what I'm going to call it is r value from a hardware store. Okay, so let's take a look at this. And what we're going to do, we're going to use a very common insulation that exists fiberglass pink. And trying to find the thermal conductivity that can be a little bit of a challenge. But anyways, I'll pull a number out. That should be pretty close. So let's say we go to the hardware store and we're going to buy some fiberglass pink. And we're told the r value is equal to 16. So what I'm going to do, I'm going to guess the thermal conductivity will not quite guess. I did look it up in a number of different tables. But let's say it's around 0.04 watts per meter degrees C. So with the r value of 16, that means that we can convert that into SI. And the way that we do that is we take our hardware store value and we divide by 5.679. And so we get 16 divided by 5.679. And when you do that, you get 2.817. So that's the r value in SI. And what we want to do, we want to find out what is the thickness of insulation that corresponds to r16. So drawing out a little schematic here, we have temperature one, temperature two, our temperature differential. We have some heat flux coming through. And this is r16. And it is, let me be correct, it is pink. So that is pink insulation. And what we're looking for here, we want to find what is the width of that. So l equals what? That is what we're trying to solve for in this example. So what we're going to do, let's write out Fourier's law. And so given our definition of r value, we said it was related to the temperature change divided by heat transfer per unit area. And that is going to be equal to l over k from Fourier's law. So that is going to equal the r value in SI. And with that, we can now solve for the length. So that's what we're after. We know this and we know that. So we can solve for it. And with that, the length is the width or thickness of this insulation. So we said the thermal conductivity for fiberglass pink was 0.038. That's an approximation. 2.817 was the r value. When we calculate, we then get 0.1071. And that's in meters. Length is 10.7 centimeters. And I am going to convert that now into inches, because in these dimensions, I think that way. Now, 4.2 inches is what we're getting. And if you look at a 2 by 4 wall, which is standard construction in North America, that is the dimensions. It's not 2 inches by 4 inches. It's 1.5 inches by 3.5 inches. So what that means is that with the thickness of 4.2, a 2 by 4 wall with 3.5 inches thick, if this thermal conductivity is correct, it would be a little less than r16. So r16 would be someplace between a 2 by 4 and maybe a 2 by 6 wall construction, provided that this value of thermal conductivity is correct for fiberglass pink. So anyways, that puts something in close proximity. So for r16, it probably could be 2 by 4 or it could be 2 by 6 construction walls. Chances are it would probably be more towards a 2 by 4. So when you see r16, that means that it's probably 2 by 4 construction. And again, you don't want to compress the insulation too much, or that will reduce the effectiveness of it. Part of the way the insulation works is it immobilizes any kind of air currents in the gap between the wall. And we'll look at that later when we talk about convection. But essentially what you want to do, you want to minimize conduction going through the wall. So the conductivity of the insulation is very low, but you also want to minimize any kind of convective air currents that might occur between the walls. So there is the wall and you have the insulation in there. So that's the way that the fiberglass pink insulation works. You have the battings and you put them in the wall. Anyways, so there is an application of r value and how it relates to thermal resistances that we're studying in heat transfer.