Ch 19: Heat and TemperatureWorksheetSee all chapters
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Ch 01: Intro to Physics; Units
Ch 02: 1D Motion / Kinematics
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Ch 19: Heat and Temperature
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Ch 35: Special Relativity
Ch 36: Particle-Wave Duality
Ch 37: Atomic Structure
Ch 38: Nuclear Physics
Ch 39: Quantum Mechanics

Concept #1: Introduction to Heat Transfer

Transcript

Hey guys, in this video we're going to talk about the different methods of heat transfer, when we started talking about thermodynamics we talked about the idea of heat being transferred between two substances that were in contact with each other that's only one type of heat transfer though we even went so far as to talk about particles colliding at the boundary between two different substances and how that transfer heat between different substances but there are other kinds of heat transfer than direct conduction and that's we're going to focus on in this video alright let's get to it. So far we've discussed a lot about the quantity of heat transfer to do things we talked about changing the phase right with latent heat we talked about changing the temperature using our M CAT equation way back when we talked about changing the size of things in thermal expansion now we need to talk about how heat is transferred and like I said we did spend some time in the beginning talking about two substances let's say A and B in direct contact where A had particles moving in random directions and every now and then A and B would have particles that would collide in the collision between them would transfer heat from one substance to the other in this case from A to B if A is hotter than B but that's only one type of heat transfer that's a heat transfer called conduction. There's also convection and lastly there's radiation. So as of right now the only type of heat transfer that we've ever been talking about is conduction the direct transfer of heat between two objects that are in contact with one another but there are still two other types to talk about. Each method of heat transfer has its own set of equations that govern how quickly or how much heat is transferred but no matter how heat is transferred the equations of calorimetry still apply so we still have our M CAT equation and we still have. Our latent heat equation those still apply no matter how an object gets the heat whether that object gets it through conduction whether it gets it through convection or whether it gets it through radiation and vice versa for how it releases heat if it releases heat through conduction through convection or through radiation those two equations still apply. So let's talk briefly about. The differences or not the differences but what in fact each of these methods entail. Conduction is the transfer of heat from one substance in contacts with another substance and this is the type of heat transfer that up to this point we've spent all of our time talking about. The direct contact leads the particle collisions along the boundary. That exchange energy from one substance to the other right that's conduction we know all about it convection is the indirect so conduction is direct contact and direct heat transfer convection is indirect transfer of heat from one substance to another and this is accomplished by heating a fluid surrounding the hot substance. A classic example is a candle OK so a candle with a flame on it heats the air in the immediate vicinity of that candle that hot fluid then rises so you can see I drew right. This thing implying that all of this hot fluid this hot air was rising up due to increased buoyancy when a fluid gets hotter the buoyancy of that fluid increases when it becomes more buoyant it starts to rise in the fluid that it's in. So the air immediately around the candle starts to heat up it's more buoyant than the air around it and it starts to rise that causes heat to go upwards. Now the problem with convection is that it's really really really complicated to talk about, it's a very complicated fluid dynamics problem and so we're not going to talk about it any more than this just what convection is but conduction and now radiation which I'm going to talk about those have simple equations that we can learn how to use and how to apply to solve problems with them that's not true for convection now radiation is the release of heat emitted via sorry of a let me start radiation is the release of heat via the emission of electro magnetic waves. Electromagnetic waves carry an energy equal to the heat lost by the substance OK so a substance is really really hot if it can radiate it will radiate electromagnetic waves and those electromagnetic waves will carry an energy equal to the heat lost by the substance like I said not every substance can emit what we would call thermal radiation I call it radiation here but the technical name is thermal radiation because there are other types of radiation too. Only certain types of substances can emit thermal radiation and we'll talk about that later. A common example of thermal radiation emission is a hot metal glowing red or white, as we can see here with this piece of whatever kind of metal it is in a blacksmith's shop the metal is heated so that it becomes pliable so they can bend it and transform it into whatever they need and when it's heated it glows and that glowing is the release of electromagnetic waves electromagnetic waves I didn't say it it's just a fancy name for light. Alright guys that wraps up our introductions to heat transfer and a brief overview of the three different types of heat transfer. Thanks for watching.

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.

Concept #3: Radiation

Transcript

Hey guys, in this video we want to talk more in detail about radiation as a method of heat transfer alright let's get to it. Remember that certain hot objects can expend heat they can emit heat in the form of electromagnetic radiation which is another word for electromagnetic waves these substances that can do it are known as Black bodies or black body like. A black body is an object that can emit the maximum amount of thermal radiation at a given temperature a black body like object will always emit less energy in the form of thermal radiation then a true black body. As with all waves a particular wave or a particular electromagnetic wave in this case is defined by its frequency it can also be defined by its wavelength but the frequency remains constant no matter what medium the wave is in whereas the wavelength changes between media so it's better to define it by frequency electromagnetic waves as I said are just a fancy way of saying light so for light a particular frequency will be referred to as its color. Visible light which is what we can see only occupies a very very small amount of the electromagnetic waves there are other types radio waves, X rays, gamma rays, microwaves etc. But for visible light the colour is absolutely dependent on the frequency and so we just extend that convention to everything even talking about X rays we'll talk about the colour of an X ray as the frequency of the light. Black bodies do not emit light at a single colour. This remember this verbing this wordage that I'm using it doesn't have to be visible light for me to say it's a single colour it could be entirely X rays and all that means is it just doesn't emit X rays at a single frequency black bodies don't emit light at a single colour they emit light across a spectrum of colours a spectrum is just a whole bunch of different colours each coming at a different probability so let me minimise myself this picture is a spectrum a black bodies spectrum of light we have in the vertical axis the brightness of the light and then the horizontal axis the frequency so the colour of the light and as you can see at low temperature. The most probable light sorry the brightest light is at a lower frequency than at a higher temperature in the visible light spectrum in light that we can see low frequency light is red moderate frequency light is yellow and high frequency light is blue that's why I showed the hotter black body as having a blue curve because the colour of light is going to be closer to blue and the cold black body emitting light as a red curve because its brightest colour is going to be closer to red. The particular shape of the spectrum what the brightest colour is how wide it is etc. Is going to be determined by the temperature of the black body the colour of the light that is seen what you will actually see is going to be the brightest colour that's going to be the one that survives and that's going to be the one that you can see as temperature increases the light shifts from red to blue. So maybe you've heard that blue flames are hotter than red flames that's typically true because for black bodies when you're emitting blue light it's because they're at a higher temperature than a black body that emits red light but there could also be a chemical process going on where the chemical that you're heating up specifically emits blue light or red light and has nothing to do with black body radiation now at very very high temperatures this spectrum shifts away from the visible light now it's so high in frequency it's no longer visible what ends up happening is the colors that you see are only the tail end of this right here this tail end that happens to be in the visible range and the combination of the colours you see is white light so at very very high temperatures when the spectrum shifts out of the visible range this light shifts from Blue which was hot black bodies to white which are black bodies that are so hot that they're emitting like ultra violet light or X rays even low energy X rays so that all that you can see because all we can see is visible light is the tail end of the spectrum right here and all of those lights are emitted at very similar brightnesses there's no clear peak brightness and a combination of colours produces white light so that's why really really hot metals glow white like we saw in the blacksmith picture when I introduced heat transfer alright now. The radiance which is something I'll talk about in a second of thermal radiation emitted by a black body like object is given by the Stefan-Boltzmann law and the Stefan-Boltzmann law the radiance is given by J the Stefan-Boltzmann law says it's equals to epsilon sigma T to the fourth. Epsilon is known as the emissivity it's how closely to a true black body a black body like object is a true black body has an epsilon of 1 all black body like objects have to have an epsilon less than 1 because they emit less light less thermal radiation than true black bodies for a given temperature. Sigma is known as the Stefan-Boltzmann constant and it has some value right here in SI units now what is radiance, radiance is the power per unit surface area of the object emitting the thermal radiation. Radiance is very very similar in its definition and it has identical units to intensity but it's different than intensity they both have the same units watts per meter squared and the best way to explain the difference is like this. Imagine the sun, the sun is emitting light, we're over here on Earth and some of that light travels all the way to Earth to reach us. What can we measure we always measure intensities of light the watts per meter squared what is the sun actually emitting that's inherent to the sun? It's emitting power which is in watts, radiance is not power intensity is power per unit area this light is being emitted whats called isotropically the same in all directions so the light creates a sphere of some radius R where R is the distance between the sun and the earth that's how big the sphere is where all the light passes through so the intensity that we measure is the power of emitted light over the surface area of that sphere which is 4 pi R squared right where R is the distance between the earth and the sun now what's the radiance, the radiance is the power emitted by the sun which is remember a unique quality of the sun, the sun emits power that's determined by internal things about the sun whereas the intensity is determined by how far away from the sun you're measuring what the radiance is is its intensity at the surface of the sun. It is the power per unit surface area of the object emitting the light so it's however much power that object is emitting divided by the surface area of that object so it's that same power but this time it's divided by the surface area of the sun and the radiance doesn't change with distance because the radiance is only measured at one point it's only measured at the surface of the object emitting the light intensity can be measured anywhere but radiance is always measured at the surface. Now the brightest colour in the emission spectrum of black body radiation or thermal radiation is given by wines or wien's displacement law and it's just B divided by T where B is wien's displacement constant and it's some value.That'll be the colour that you see if it's in the visible light region if it's past the visible light region you're going to see white light instead. Let's do a problem. A spherical object of 0.01 meter radius with an emissivity of 0.8 is heated to a temperature of a 1000 kelvin how much heat is radiated by this object in 5 milliseconds? What is the brightest color of this emission? So I'm going to call this A and I'm going to call this B. So part A we're talking about thermal emission so we're going to have to use the Stefan–Boltzmann law first so the Stefan–Boltzmann law is the radiance equals the emissivity times the Stefan–Boltzmann constant times the temperature to the fourth power the emissivity is 0.8. The temperature is the 1000 kelvin and the Stefan–Boltzmann constant is just a constant so this is 0.8. The Stefan–Boltzmann constant is 5.67 times 10 to the negative 8 and the temperature is a 1000 kelvin if it was given in Celsius you have to convert it to kelvin this is an absolute temperature this is not a difference in temperatures so degrees Celsius and kelvin not the same unit and this is to the fourth power. So the radiance is going to be 45360 watts per square meter now we want to know how much heat is radiated by this object in 5 meters per second well what does the radiance tell us the radiance tells us the power emitted by the object at the surface of the objects OK. So the power is going to be the radiance sorry. It's going to be the radiance times the surface area of the objects. Remember the power is the radiance at the surface of the object so we already have the radiance 45360 in our SI units this is a spherical object so the surface area of the sphere is 4 pi R squared the radius is 0.01 squared so the power is 57 watts now what we want to know is how much heat is radiated in 5 milliseconds well now that we know the power which is the amount of heat per second we can simply say that the heat is the power times the amount of time which is 57 watts times 0.005 that's 5 milliseconds and that is going to be 0.285 joules. That wraps up our discussion on thermal emission and radiation as a form of heat transfer. Thanks for watching guys.

Practice: If the intensity of sunlight measured at the Earth’s surface is 1400 W/m2 , what is the surface temperature of the Sun? Treat the Sun like a true blackbody. Note that the distance from the Earth to the Sun is 1.5 x 1011 m and the radius of the Sun is 696 million meters.