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Ch 21: Heat and TemperatureWorksheetSee all chapters

# Heat Transfer

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Sections
Temperature
Linear Thermal Expansion
Volume Thermal Expansion
Specific Heat & Temperature Changes
Latent Heat & Phase Changes
Intro to Calorimetry
Calorimetry with Temperature and Phase Changes
Advanced Calorimetry: Equilibrium Temperature with Phase Changes
Phase Diagrams, Triple Points and Critical Points
Heat Transfer

Concept #1: Introduction to Heat Transfer

Transcript

Concept #2: Conduction

Transcript

Hey guys, in this video we're going to talk about conduction in more detail well 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. 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, when studying calorimetry all heat transfers were via conduction and that was another point that I made when you put two objects in thermal isolation together in contact the heat transfers always going to be conduction. 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. Materials have a natural allowance for heat flow known as the thermal conductivity. Given by K it's how easily they allow heat to be transferred quickly through them the larger the thermal conductivity the faster heat is conducted. So materials with a high are called thermal conductors and material with low thermal conductivity are called thermal insulators. Now when dealing with heat we talk often about a heat current, the current for the heat is just how rapidly the heat is moving per second so its just Q over delta T we've seen problems before that says heat was entering at 95 joules per second that was the heat current. How much energy per second ? So the conduction current is the heat current for conduction all right let me minimise 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'll just call cold and a connection between the two this is the conducting material this is the conductor and the conductor is 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 about these systems. The conduction current through the conductor is going to be given by K times A times the hot temperature minus the cold temperature over L 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 surface I explained that, lets move past that. The heat conducted will then just be given by H times delta T 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. Now notice H should not be a constant the conduction current should absolutely change as the hot substance became colder because its releasing heat and the cold substance becomes hotter so naturally this is going to drop and this is going to go up that's what happens as heat goes 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, what a reservoir is for anything and we use that a lot in thermodynamics is a reservoir is an infinite source or sink of heat that means that it can absorb and release an infinite amount of heat without changing its temperature one bit. That's what it means to be a reservoir so if we look at our conduction current equation imagine now that the hot object and the cold object were reservoirs and the conductor was 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 we 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 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 long piece of iron with a 0.05 square meter cross-section how much heat crosses the piece of iron in 5 seconds ? And then it gives us the thermal conductivity of iron so we're talking about how much heat in some amount of time so we know we need to use Q equals H delta T and we know that H the conduction current is K A, T H minus T C over 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 a 100 degrees Celsius minus 0 degrees Celsius 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 because there is 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. Divided by the length and we're told that it's a 15 centimeter long piece of iron So this is 0.15 meters plugging all of that in the heat current is 2650 watts. Joules per second is what I gave is a units for conduction current but a joule per second is just a watt so most of the time conduction current is given in watts, 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 there temperatures don't change and therefore H doesn't change so this is 2650 times we were asked for it in 5 seconds and so this is 13250 joules or 1.33 kilojoules like I said typically like to give these units in kilojoules because most of the problems ops this is not it's 13.3, 13.3 kilojoules because most of these heats are large enough to be represented as kilojoules and to 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.

Practice: A cubic Styrofoam cooler containing ice on a hot day is shown in the following figure. The thickness of each wall of the cooler is 15 mm, with a side length of 1 m. If it is 40°C outside, how long will 2 kg of ice last in the cooler? Assume that during the melting process, the temperature inside the cooler remains at 0°C and that no heat enters from the bottom of the cooler. Note that the latent heat of fusion for water is 334 kJ/kg and the thermal conductivity of Styrofoam is 0.033 W/mK.