Temperature - Online Tutor, Practice Problems & Exam Prep

Temperature is a measure of how hot or cold something is, related to the average kinetic energy of particles. The three main temperature scales are Fahrenheit, Celsius, and Kelvin. The freezing and boiling points of water serve as reference points: 0°C (32°F) and 100°C (212°F) for Celsius and Fahrenheit, respectively. The Kelvin scale starts at absolute zero (0 K), equivalent to -273.15°C. Key conversion equations include: $T$_F=95T_C+32 and $T$_C=59(T_F-32).

Introduction To Temperature Scales

Hey, guys. So, for the next couple of chapters, we're going to start talking about thermodynamics. To start things off, we're going to talk about the most basic fundamental measurement within thermodynamics, which is called temperature. I want to give you an introduction, a brief introduction, on temperature and the different scales and systems that we use in physics. Let's go ahead and check this out here.

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. 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 very cold, whereas if you stick your hand in a pot of boiling water, that, unfortunately, is going to be very painful and feel very hot. These aren't really precise scientific definitions. So, a more useful one is that it's related to the average kinetic energy of the particles that make up an object. Remember that kinetic energy is related to how fast particles are moving. The idea here is that the molecules of water that are locked up inside of an ice cube are vibrating very slowly. They have 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 moving around very quickly. So, there's a high temperature, the things feel very hot, so there's lots of kinetic energy and the particles are moving very fast.

We're going to have to do some measurements and calculations with temperature. So, we're actually going to need to know the 3 temperature scales or systems of units that we have in physics, and they're all actually related to 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 scientist 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. The Fahrenheit scale has two reference points: the freezing point of water is 32 degrees Fahrenheit and the boiling point is 212 degrees Fahrenheit exactly. Now, there are obviously much colder temperatures. The zero point is going to be somewhere around here, all the way down to the coldest temperature possible. We'll talk 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 scientists did is we called the freezing points, the point where ice turns to water and vice versa, the 0 point. This is where 0 degrees Celsius is, and the boiling point, this is actually 100 degrees Celsius. So, what I want to point out is that these measurements mean the exact same thing. So, for instance, 0 degrees Celsius and 32 degrees Fahrenheit both represent the freezing point of water. We're just naming them; we're sort of calling them different numbers. It's kind of how 12 inches is equal to 1 foot. They both represent the same distance just on different number scales. It's the same exact idea here.

The last thing I want to talk about is the Kelvin scale. The Kelvin scale is the one that we're going to use most commonly. It's the one that we're going to plug into all of our equations. We're going to 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 0 as the freezing point of water, and in the Fahrenheit scale, 0 was just sort of over here somewhere. It 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. This is actually what we define as the beginning of the Kelvin scale. It's the coldest possible temperature that you could ever have.

The freezing point in Kelvin is going to be 273.15 Kelvin and the boiling point is going to be 373.15 Kelvin. What I want you to realize is that the difference between these two numbers is 100. The difference between these two numbers is also 100. So, the Kelvin and Celsius scales are actually sort of the same, it's just that one is shifted downwards like this. Whereas this scale over here, the Fahrenheit, these differences are actually 180. So, basically, you can kind of think about it that the scale is a little bit bigger. There are more numbers in between those freezing and boiling points.

We can actually go ahead and convert the coldest temperature possible to Celsius. It's going to be negative 273.15 degrees Celsius, and in Fahrenheit, it's going to be negative 459.67 degrees Fahrenheit. Again, all these measurements mean the same thing. These are all the coldest possible temperatures just in their respective scales. Hopefully, this makes sense. Let me know if you guys have any questions.

How To Convert Between Temperature Units

Hey guys. In an earlier video, we talked about all the different temperature units that we are going to use in thermodynamics. We talked about Fahrenheit, Celsius, and Kelvin. Now, in some problems, you are going to 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 going to show you how to do that in this video, how to convert between the different temperature units, and we're just going to 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 asked for Fahrenheit, you don't have to do anything, right? There's no conversion. It's the same thing for Celsius and Celsius or Kelvin and Kelvin. There are no conversions 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 \( \frac{9}{5} TC + 32 \). Now I'm going to go in a little bit of a different order because it turns out that when you go diagonally across this table, the equations are going to 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 we have to do is just take this equation and then solve for \( TC \), and what you would get is you would get \( \frac{5}{9} \left(TF - 32\right) \). You can pause the video and see if you can actually work out and get the same answer.

Right. So we're going to calculate, we're actually going to talk about these equations in just a second here. We're going to go ahead and skip to these 2. So a very common one you're going to 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 0. So a change of 1 Kelvin is the same thing as a change of 1 Celsius. So these equations are actually very straightforward and they're very related to each other. All we have to do is just do \( TK - 273.15 \), 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 \( TK \) and you're going to get \( TC + 273.15 \).

Right? So all you have to do is just shift back and forth, from the absolute 0. Alright. So now, finally, this Kelvin to Fahrenheit and vice versa. So we want a Kelvin to Fahrenheit. This equation here is going to be \( \frac{9}{5} \left(TK - 273.15\right) + 32 \). This might seem really complicated, but all that's really happening here is you're actually just sort of merging these two equations together, you're sort of combining them. You got the \( \frac{9}{5} \), and all that happens here is we're sticking this expression in for \( TC \). So if you do that, you're basically just going to get this equation over here. Now the opposite equation to get from Fahrenheit to Kelvin, basically you're just going to go ahead and solve for this \( TK \), and it's going to be \( \frac{5}{9} \left(TF - 32\right) + 273.15 \).

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 are a lot of equations here, is really just these two equations. If you remember these 2, 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 are given a temperature that's in Celsius, and we want to convert it to Kelvin. That's going to be in part a. So we have negative 196 degrees, and we want to figure out what that is in Kelvins. Alright, so basically, we're given Celsius and we're asked for Kelvin, so we're just going to use this equation over here. So this is \( TK = TC + 273.15 \). So this is going to be \( TK \), our temperature at Kelvin, is going to be negative 196 degrees Celsius plus 273.15, and what you're going to get is you're going to get 77.15 Kelvin. Notice how this is a positive number, and we should always get positive numbers for Kelvin. We can never have something that's negative Kelvin, right? Because the lowest temperature is absolute 0.

Alright, so -196 is actually 77.15 Kelvins, 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 196 to Fahrenheit, so we have Celsius to Fahrenheit. So now we're just basically going to use this equation over here: Given Celsius, asked for Fahrenheit. So this is going to be \( TF = \frac{9}{5} TC + 32 \). So this is going to be \( TF = \frac{9}{5} \cdot \left(-196 +32\right) \), and what you're going to get here is, you're going to get negative 320.8 degrees Fahrenheit.

Alright, so that's the answer to that one. Now, one really minor point just in case your professor is super picky about this: whenever you're expressing a temperature in Fahrenheit, you're always going to write degrees Fahrenheit. Anytime you're representing something in Kelvin, you don't have to put the degree symbol, you just write k. It's just kelvins. Alright. That's it for this one, guys. Let me know if you have any questions.

The 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. a) 8276°C
  b) 8549 K
• C. a) 2527°C
  b) 2800 K
• D. a) 4853°C
  b) 2728 K

Converting Between Celsius and Fahrenheit

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 these Celsius and Fahrenheit scales, remember that 0 degrees Celsius is equal to 32 degrees Fahrenheit. We've seen that before. Another one sort of special number that we saw is that 100 degrees Celsius is equal to 212 degrees Fahrenheit. 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 gonna 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. Alright? 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 2 variables in here, but I know that these two variables are gonna 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 with just a single t, just one variable. So what that means is that t is equal to 9/5 t 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, what we can do is we have t 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, and minus 9/5 off from this side but then I have to move it over to this side. So I have to subtract 9/5 t and this is gonna be 32. Now what happens here, I've got T minus 9/5 T. Now the only way I can subtract these 2 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 5/5 t. 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 this step is this is just gonna be negative 4/5 t equals 32. Now I've just got one last step to do. I just have to divide by this negative 4/5 t. 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 t is equal to negative 40 degrees. So what that means is that negative 40 degrees Celsius is equal to negative 40 degrees Fahrenheit. 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 40 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.

Here’s what students ask on this topic:

What is the definition of temperature in physics?

In physics, temperature is defined as a measure of how hot or cold something is. More precisely, it is related to the average kinetic energy of the particles that make up an object. The faster the particles move, the higher the temperature. For example, in a pot of boiling water, the water molecules move very quickly, indicating a high temperature. Conversely, in an ice cube, the molecules vibrate slowly, indicating a low temperature.

What are the three main temperature scales used in physics?

The three main temperature scales used in physics are Fahrenheit, Celsius, and Kelvin. The Fahrenheit scale is commonly used in the United States, with the freezing point of water at 32°F and the boiling point at 212°F. The Celsius scale, used worldwide, has the freezing point of water at 0°C and the boiling point at 100°C. The Kelvin scale, used in scientific contexts, starts at absolute zero (0 K), equivalent to -273.15°C, and is used for most thermodynamic calculations.

How do you convert Celsius to Fahrenheit?

To convert Celsius to Fahrenheit, you can use the following equation:

$T{F}_{}=\frac{9}{5}T{C}_{}+32$

For example, if you have a temperature of 25°C, you can convert it to Fahrenheit as follows:

$T{F}_{}=\frac{9}{5}\left(25\right)+32=77$

What is absolute zero?

Absolute zero is the lowest possible temperature, where the kinetic energy of particles is minimal. It is defined as 0 Kelvin (K), which is equivalent to -273.15°C or -459.67°F. At absolute zero, particles theoretically stop moving entirely, and no further thermal energy can be extracted from the substance. This concept is fundamental in thermodynamics and helps define the Kelvin temperature scale.

How do you convert Kelvin to Celsius?

To convert Kelvin to Celsius, you can use the following equation:

$T{C}_{}=T{K}_{}-273.15$

For example, if you have a temperature of 300 K, you can convert it to Celsius as follows:

$T{C}_{}=300-273.15=26.85$

Why is the Kelvin scale considered an absolute temperature scale?

The Kelvin scale is considered an absolute temperature scale because it starts at absolute zero, the lowest possible temperature where particles have minimal kinetic energy. Unlike the Celsius and Fahrenheit scales, which are based on arbitrary reference points like the freezing and boiling points of water, the Kelvin scale is based on a fundamental physical limit. This makes it particularly useful in scientific calculations and thermodynamics.