20. Heat and Temperature

Temperature

1

concept

## Introduction To Temperature Scales

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Hey guys, over the next couple of chapters, we're gonna start talking about thermodynamics. And to start things off, we're gonna start talking about the most basic fundamental measurement within thermodynamics, which is called temperature. So, I'm gonna give you an introduction of brief introduction on temperature and the different scales and systems that we use in physics. Let's go ahead and check this out here. So, what is temperature? Well, we're going to develop a much more precise definition later on. But for now, a basic definition of temperature is it's a measure of how hot or cold something is. So, we can kind of rely on our everyday experience for this. If you grab an ice cube, that ice cube relative to you is probably feels very cold. Versus if you stick your hand in a pot of boiling water that unfortunately is gonna be very painful and feel very hot. Now, these are really precise scientific definitions. So, a more useful one is it's a measure or it's related to the average kinetic energy of the particles that make up an object. So, remember that kinetic energy is related to how fast particles are moving. So the idea here is that the molecules of water that are sort of locked up inside of an ice cube are vibrating very slowly. There are low temperature, they don't have a lot of kinetic energy and therefore the particles move relatively slowly versus the pot of boiling water. These things are actually moving around very, very, very quickly. So there's a high temperature. The things feels very hot. There's lots of kinetic energy and the particles are moving very fast. All right, so we're gonna have to do some measurements and calculations with temperature. So we actually need to know the three temperature scales or systems of units that we have in physics. And they're all actually related on arbitrary reference points that have to do with water. These are basically just values that we picked because we could easily reproduce them. These are things like the freezing point or boiling point of water. Basically any scientists could freeze or boil water and that's what we chose as our reference points. So if you live in the United States, you're probably most familiar with the Fahrenheit scale and the Fahrenheit scale has two reference points. The freezing point of water is 32 F and the boiling point is 212 F exactly. Now there are obviously much colder temperatures. Zero point is gonna be somewhere around here all the way down to the coldest temperature possible. We're talking about that in just a second here. Now, the other scale that we use is called the Celsius scale. Basically, if you live anywhere else in the world, you probably use this one. This is sort of like the metric system temperature scale and the reference points that we use are a little bit more intuitive basically what scientist is did is we called the freezing points. The point where ice turns to water and vice versa. We call this the zero point, this is where zero Celsius is and the boiling point. This is actually 100 degrees Celsius. So I don't want to point out is that these measurements mean the exact same thing. So for instance, zero degrees Celsius and 32 F both represent the freezing point of water. We just naming them, we're sort of calling them different numbers. It's kind of how like 12 inches is equal to one ft, they both represent the same distance, just on different number scales. It's kind of the same exact idea here. Alright, so the last thing I want to talk about is the kelvin scale. The kelvin scale is the one that we're gonna use most commonly, it's the one that we're gonna plug in to all of our equations, we're gonna plug in all of our temperatures in kelvin. Now, kelvin is a little bit different because it's called an absolute temperature scale. The reason it's called this is that the kelvin scale actually starts at absolute zero. What do I mean by that? Well, for the Celsius scale we just chose zero as the freezing point of water and in the Fahrenheit scale, zero was just sort of over here somewhere doesn't actually correspond to anything special, but for the kelvin scale, the absolute zero, the zero point, the starting point is the coldest temperature possible. So this is actually what we define as the beginning of the kelvin scale, it's the coldest possible temperature that you could ever possibly have. Alright, and so we call this absolute zero. So the freezing point of in kelvin is gonna be 273. kelvin and the boiling point is going to be 73.15. Alright, so what I want you to do is realize that these scales here, the difference between these two numbers is 100. The difference between these two numbers is also 100. So the kelvin and Celsius scale are actually sort of the same, it's just that one is sort of shifted downwards like this. Whereas this scale over here, the Fahrenheit, these differences are actually 100 eighty's. So basically you can kind of think about is that the scale is a little bit bigger. The numbers there are more numbers in between those freezing and boiling points. Alright, so we can actually go ahead and convert the coldest temperature possible to Celsius, that's gonna be negative to 73.15 degrees Celsius and Fahrenheit, it's gonna be negative for 59.6 degrees Fahrenheit Again, all these measurements mean the same thing, These are all the coldest possible temperatures just in their respective scales. Alright, so hopefully this makes sense. Let me know if you guys have any questions

2

concept

## How To Convert Between Temperature Units

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Hey guys, in an earlier video, we talked about all the different temperature units that we're gonna use in thermodynamics? We talked about Fahrenheit, Celsius and kelvin Now, in some problems you're gonna have to convert between these different temperature units. Some problems will give you a measurement in one unit, like Celsius and you'll have to convert it to another one like kelvin or even Fahrenheit. So I'm gonna show you how to do that in this video, how to convert between the different temperature units. And we're just gonna use this table of equations right here. It's very straightforward to use all we have to do is just locate which units were given which ones we are asked to calculate or asked to convert to and then just use the appropriate equation. So let's go ahead and get started here. So obviously if you are given Fahrenheit and Astro Fahrenheit, you don't have to do anything. Right, there's no conversion, it's the same thing for Celsius and Celsius or Calvin and Calvin, there's no convergence. You have to do where things are a little bit different is if you are given Celsius and then asked for Fahrenheit. So let's take a look at that equation here. So TF the Fahrenheit temperature is going to be 9/5 TC plus 32. Now I'm gonna go in a little bit of a different order because it turns out that when you go diagonally across this table, the equations are gonna be related. So for example, what if I had the opposite, what if I was given Fahrenheit and then asked for Celsius. Now it's the reverse. All you have to do is just take this equation and then solve for T. C. And what you would get is you would get 5/9 and then T f minus 32. You can pause the video and see if you can actually work out and get the same answer. Alright so we're gonna calculate we're actually gonna talk about these equations in just a second here we're gonna go ahead and skip to these two. So a very common one you're gonna have to do is convert between kelvin and Celsius and vice versa. Remember that the kelvin scale and the Celsius scale are the same it's just that one of them is sort of shifted to absolute zero. So a change of one Kelvin is the same thing as a change of one C. So these equations are actually very straightforward and they're very related to each other. All you have to do is just do T k minus 73.15 and that's how you get to Celsius. So if you wanted the opposite equation, if you had Celsius and you wanted kelvin then you would just solve this equation for T. K. And you're gonna get T c Plus to 73.15 right? So all you have to do is just shift back and forth from the absolute zero. Alright so now finally this kelvin to Fahrenheit and vice versa. So we want to kelvin to Fahrenheit, this equation here is gonna be 9/5 T k minus 2, 73.15 plus 32. This might seem really complicated but all really it's happening here is you're actually just sort of merging these two equations together, you're sort of combining them, you got the ninth fist and all that happens here is we're sticking this expression in for T. C. So if you do that, you're basically just gonna get this equation over here. Now, the opposite equation to get from Fahrenheit to kelvin, basically you're just gonna go ahead and solve this T. K. And it's gonna be 5/9 then T f minus Plus to 73.15. So again this equation here is really just a combination of these two equations. So all you really have to memorize, it might look like there's a lot of equations here is really just these two equations. If you remember these two you can get to any of the other ones basically just by flipping some of the variables. Alright, so that's all you really need to know. Let's go ahead and take a look at our example. So we're given a temperature that's in C and we want to convert it to Kelvin that's going to be in part a so we have negative 196° and we want to figure out what is that in kelvin's. Alright, so basically we're given Celsius and were asked for kelvin, So we're just gonna use this equation over here. So this is T. K equals T. C. Plus to 73.15. So this is gonna be T. K. Are temperature in kelvin is gonna be negative 1 96 degrees Celsius Plus to 73.15. And what you're gonna get is you're gonna get 77. kelvin. Notice how this is a positive number and we should always get positive numbers for kelvin. You can never have something that's negative kelvin, right? Because the lowest temperature is absolute zero. Alright, so negative 1 86 is actually 77.15 kelvin's and that's the answer to part A So now let's take a look at the second one. Now we want to convert negative 1 96 2. Fahrenheit. So we can have Celsius to Fahrenheit. So now we're just basically gonna use this equation over here, were given Celsius asked for Faron heights. So this is gonna be T. F. Equals 9/5 TC plus 32. So this is gonna be T. F equals 9/5. Uh This is gonna be let's see uh negative 1 96 plus 32. And what you're gonna get here is you're gonna get negative 320.8 degrees Fahrenheit. All right, so that's the answer to that one. No one really minor point just in case your professor super picky about this whenever you're expressing a temperature in Fahrenheit, you're always going to be right degrees Fahrenheit, anytime you're representing something in kelvin, you don't have to put the degree simple, you just write K. It's just kelvin's alright. That's it for this one. Guys, let me know if you have any questions.

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Problem

ProblemThe tungsten filaments inside of most incandescent lightbulbs reach temperatures of about 4580°F when the lightbulbs are lit. What is this temperature in a) Celsius and b) Kelvin?

A

a) 2527°C

b) 2785 K

b) 2785 K

B

a) 8276°C

b) 8549 K

b) 8549 K

C

a) 2527°C

b) 2800 K

b) 2800 K

D

a) 4853°C

b) 2728 K

b) 2728 K

4

example

## Converting Between Celsius and Fahrenheit

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Hey guys got a pretty interesting problem here. This is a pretty common one that pops up. We're gonna calculate the one magical temperature where the Celsius and Fahrenheit scales are equal to each other. So if you know anything about the Celsius and Fahrenheit scales, remember that zero degrees Celsius is equal to 32 F, We've seen that before. Another one sort of special number that we saw Is that a 100°C is equal to 212 F. So if you look what's happening here, we grow 100. So you're growing 100 degrees in the Celsius scale, but you're growing 180 degrees in the Fahrenheit scale. So basically what happens is that the Fahrenheit scale grows a little bit faster than the Celsius scale. And what happens is if you work backwards, there's going to be one magical temperature where the two numbers are equal to each other. So basically what that means, if I can sort of put that in terms of variables, is that T. C. Is gonna equal T. F the same number. The number in Celsius is gonna be the same exact number in Fahrenheit. So then how do we solve for this magical number here? We're gonna need an equation that relates these two variables together. So basically what that means is that on our conversion table, we can either be given Celsius or ask for Fahrenheit, which means we'll be using this equation or we can work the other way, we can be given Fahrenheit and asked for Celsius in which we'll use this equation. You just need one equation that relates the Fahrenheit and Celsius scales. So either one of these will work. Now I think this one does a little bit easier because this equation has a parenthesis in it. But just in case you did pick that you can actually just go ahead and get the same answer with that. All right, so let's get started here, basically what this means is that T. F is gonna equal 9/5 T. C plus 32. Now, what happens is I have two variables in here, but I know that these two variables are going to be the same exact number. The whole point of this problem is that we're looking for the one temperature in which these two things are equal to each other. So what I can do is I can just replace both of these variables was just a single T. Just one variable. So what that means is that T is equal to 950 Plus 32. Now, all I have to do is really just solve for this t here, that's the one number in which these two things will be equal to each other. Alright, so really this is just a couple of algebra steps, basically we can do as we have tea on one side and t on the other. I want to subtract this over here but I've got a fraction in here. So what I have to do is I'm gonna do t I'm gonna minus 9/5 off from this side but then I have to move it over to this side. So I have to subtract 9 50 this is going to be 32. Now what happens here? I've got t minus 9 50. And the only way I can subtract these two is if I make the denominator the same, so this is just one T. So I can convert this to a fraction by just saying that this is 5 right? That's the same thing. All I'm doing here is I'm just making these denominators equal to each other. So if you work out with this step is this is just gonna be negative 4 50 equals 32. Now I've just got one last step to do, I just have to divide by this negative 4 50. So I'm gonna divide by negative 4/5 over here and then I have to do the same thing to the other side. And then basically what you end up with, is that a. T. Is equal to negative 40 degrees. So what that means is that negative 40 degrees Celsius is equal to negative 40 F. Now there's one really easy way that you can check for this, This is basically what the answer is all you have to do is just plug in negative into this equation. And then what you'll get here is negative 40. So those two things are going to be equal anyway, so that's it for this one, guys, let me know if you have any questions.

Additional resources for Temperature

PRACTICE PROBLEMS AND ACTIVITIES (3)

- Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Ranki...
- (b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other
- (a) Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.