Hey guys. In this video, we're going to talk about conduction in more detail. While we've talked about conduction in the qualitative sense, the conceptual sense, we haven't used any equations to describe conduction. Specifically, how quickly can heat be conducted from one object to another. Alright, that's what we're going to focus on in this video. Let's get to it. Remember that conduction is the transfer of heat through direct contact. Okay? Conduction is the most common type of heat transfer you're going to encounter in your studies, in your introductory physics courses. That's why conduction was basically the only type of heat transfer that we've seen up to this point. Okay? When studying calorimetry, all heat transfers were via conduction. Okay, and that was another point that I made. When you put two objects in thermal isolation together in contact the heat transfer is always going to be conduction. Okay? What we're interested in is how rapidly heat can be conducted from a hot substance to a cold substance, right? It always goes from hot to cold, and we're going to get to that later on when we cover the second law of thermodynamics. But we want to know how quickly this happens, how long it takes to happen. Okay? Materials have a natural allowance for heat flow known as the thermal conductivity, given by k. Okay, it's how easily they allow heat to be transferred quickly through them. Okay, the larger the thermal conductivity, the faster heat is conducted. Okay, so materials with a high thermal conductivity are called thermal conductors, and materials with low thermal conductivity are called thermal insulators. Alright.
Now when dealing with heat, we talk often about a heat current. Okay? The current for the heat is just how rapidly the heat is moving per second. Okay? So it's just q ∕ Δ t. We've seen problems before that says heat was entering at 95 joules per second. That was the heat current. Okay? How much energy per second. Okay? So the conduction current is the heat current for conduction. Alright, let me minimize myself. We have two substances here. We have one at a hot temperature, one at a high temperature which we just call hot, and one at a low temperature which we just call cold, and described by three things. It's got a cross-sectional area, it's got a length, and not written here, it has a conductivity. Those are the three aspects that describe the conductor. Besides that, you also have the temperature of the hot substance and the temperature of the cold substance which have nothing to do with the conductor. Those are the conductor. Given by k ⋅ a ⋅ (hot temperature − cold temperature) ÷ l. Okay, and this is a very important equation, and the units are going to be joules per second because it's just the amount of heat transferred per second. Alright? There are a few important consequences of this equation. First, the conduction current, like I said, is the rate at which heat is conducted through the surface. There was a substance. Okay. I explained that. Let's move past that. The heat conducted would then just be given by h ⋅ Δ t. Okay, as long as h is a constant. If h is not a constant, then you couldn't just multiply it by the amount of time because h might change as that time goes on. If you knew the average conduction current, you could multiply it by the amount of time and find the total heat transfer, but this equation right here typically only works if h is a constant. Okay? Now notice h should not be a constant. Okay. The conduction current should absolutely change as the hot substance became colder because it's releasing heat, and the cold substance becomes hotter. So naturally, from the hot substance to the cold substance. So h should not be a constant. The conduction current will be constant if the hot and cold substances are what we call reservoirs. Like a reservoir of water. A reservoir of water is a giant source of water. Okay? What a reservoir is for anything, and we use it a lot in thermodynamics, is a reservoir is an infinite source or sink of heat. That means it can absorb and release an infinite amount of heat without changing its temperature one big. Okay? That's what it means to be a reservoir. So if we look at our conduction current equation, imagine now that the hot objects and the cold objects were reservoirs, and the conductor and the conductor were connected between the two reservoirs, then no matter how much heat went through the conductor the temperature of the reservoirs would never change. That's the point of being a reservoir. It's an infinite source so it can produce as much heat as it wants. It's an infinite sink so it can absorb as much heat as it wants, all without leading to any change in temperature. So if this substance and this substance here were reservoirs, then the conduction current through the conductor would, in fact, be a constant. Okay? And that's an important point to make because you'll probably see reservoirs quite a bit in thermodynamics. Alright, let's do an example. A hot reservoir at 100 degrees Celsius is connected to a cold reservoir at 0 degrees Celsius by a 15 centimeter piece of iron in 5 seconds? And then it gives us the thermal conductivity of iron. Okay, so we're talking about how much heat in some amount of time. So we know that we need to use q = h ⋅ Δ t. Okay? And we know that h, the conduction current, is k ⋅ a ⋅ 100 − 0 ÷ l. We're told that the hot source and the cold source are actually reservoirs in this problem. A hot reservoir and a cold reservoir. So the conduction current is going to be constant. Let's calculate that. The thermal conductivity of iron is 79.5, and the units of watts per meter-kelvin are SI units. The cross-sectional area is 0.05. The hot reservoir is 100 degrees Celsius minus 0 degrees Celsius. Okay? Now, because this is a change in temperature, this is a difference in temperature, right? You have a hot minus a cold. Even though there's no delta there, because there's a change in temperature, we can simply leave this in degrees Celsius because that change in Celsius is equivalent to a change in Kelvin. And we do need Kelvin because if you notice the SI unit right here is Kelvin, okay, divided by the length, and we're told that it's a 15-centimeter long piece of iron. So this is 0.15 meters. Okay? Plugging all of that in, the heat current is 2650 watts. Okay, joules per second is what I gave it as the units for conduction current, but a joule per second is just a watt, so most of the time, conduction current is given in watts. Okay, now we can find the total heat transferred, and we're perfectly allowed to use this equation because since the hot source and the cold source are reservoirs, their temperatures don't change and therefore for h doesn't change. So this is 2650 times, we were asked for it in 5 seconds, And so this is 13,250 joules or 13.3 kilojoules. Like I said, typically like to give these units in kilojoules because most of these heats are large enough to be represented as kilojoules and too large to be represented as joules. Alright, that wraps up our discussion on the conduction current and conduction in specific. Alright? Thanks for watching, guys.
