Video: The Kelvin Temperature Scale

In this lesson, we will learn how to convert between the Celsius and Fahrenheit scales and the kelvin scale, and define absolute zero.

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Video Transcript

In this video, we’re talking about the kelvin temperature scale. Along with the Fahrenheit and Celsius temperature scales, the kelvin scale is one of the most commonly used. Even more than that, the SI system accounts the kelvin as the base unit of temperature. So, let’s learn where the kelvin temperature scale comes from, as well as how to convert temperatures to and from the scale. When we think about scales of temperature, one of the earliest that became popular is called the Fahrenheit scale.

The Fahrenheit scale is set up so that the temperature at which water boils, at which it goes from a liquid to a gas, is 212. And then on the same scale, the temperature at which water freezes is 32. For historical reasons, readings on the Fahrenheit scale were described in terms of degrees, so water boils at 212 degrees Fahrenheit and it freezes at 32 degrees Fahrenheit. So, this is the Fahrenheit temperature scale, and it became popular, partly, because Fahrenheit was such a good builder of accurate thermometers. Many scientists and inventors used his thermometers, and so this scale became the standard way of describing temperatures. Eventually, though, an idea for a new scale was developed.

The Swedish astronomer, Anders Celsius, wanted to develop a scale that used the same marking points, the boiling and freezing points of water, respectively. But he wanted these temperatures to appear at either end of a centigrade scale. That is, a scale divided up into 100 even parts. So, on what came to be called the Celsius scale, water boiled at a temperature of 100 and it froze at a temperature of zero. And like the Fahrenheit scale, the Celsius scale inherited this way of describing temperatures in degrees. So, 100 degrees Celsius is where water boils and zero degrees Celsius is where it freezes.

Now, if we look at this temperature scale in its current form, it seems to indicate that there is neither a maximum nor a minimum temperature that an object can have. That is, it seems that an object could be as hot or as cold as we could imagine without limit in either direction. But this idea began to be challenged as scientists did more and more research work with gases. Specifically, researchers were looking at the way that gas volume, the space that a gas takes up, varies with the temperature of the gas. Over a certain range of temperatures, the temperatures the researchers could access in their experiments, the trend that appeared was the colder the temperature of the gas, the less space it took up. And this raised the question: if the volume of a gas was brought all the way down to zero, what would its temperature be?

One way to get an idea for this temperature is to draw a line of best fit through the available data and follow it to where it would cross the horizontal axis. It was at this temperature where the volume of the gas was predicted to be zero. That is, it was predicted to take up no space. Now, no one had ever actually measured this temperature. But there were different predictions as to what its value was. Some predicted this value to be around negative 250 degrees Celsius. Others said it was much lower, more like negative 3000 degrees Celsius. Regardless of the particular predicted value, people agreed that the name of this temperature was absolute zero, that it was the lowest temperature a gas or any other object could have.

Based on this realization, researchers realized that there was a lower end to the temperature scale. If predictions about absolute zero were correct, the new temperature could be lower than it. The scale would stop. Once this lower limit was recognized, it made sense that it was time for a new temperature scale, and this is where the researcher, William Thomson, comes in. Thomson, later named Lord Kelvin, developed a temperature scale that starts at this minimum possible temperature, absolute zero. And Kelvin, naturally enough, assigned the value of zero for this minimum. This means that on this scale, what’s called the kelvin temperature scale, all temperatures are either positive or zero. Nothing can be negative.

One other update Kelvin made as he developed his scale was that he did away with the idea of degrees. On the kelvin temperature scale, temperatures are referred to by their value and then the unit, kelvin. For example, the temperature of absolute zero on the kelvin scale is not zero degrees kelvin, but simply zero kelvin. Over time, as experimental procedures improved, the distance in temperature between absolute zero and the temperature at which water freezes was determined more accurately. It turns out that the freezing point of water is 273 kelvin. And then, because a change in temperature of one kelvin is the same as a change in temperature of one degree Celsius, that means that the boiling point of water, 100 degrees Celsius, is 373 kelvin.

That is, just as there is an increase of 100 degrees Celsius between the Celsius temperatures, so there is an increase of 100 kelvin between the kelvin temperatures. And this means, by the way, that absolute zero in degrees Celsius is negative 273. So, zero kelvin and negative 273 degrees Celsius are the same temperature just on different scales. And this correspondence gives us a clue as to how to convert between temperatures in the Celsius scale and the kelvin scale. Let’s say we’re given a temperature in degrees Celsius, and we’ll call that 𝑇 sub C. Well, if we add 273 to that temperature in degrees Celsius, it will give us the equivalent temperature in kelvin.

For example, let’s say we’re talking about the temperature at which water freezes, zero degrees Celsius. So then, 𝑇 sub C in this equation is equal to zero. We’ll leave off units, as we do whenever we convert temperatures across different scales. So, we have zero plus 273 and that’s equal to 273. And looking back over at our scale, we see that, indeed, the temperature at which water freezes is 273 kelvin. So then, this is the recipe or the equation for converting between the kelvin and Celsius scales. But what if we had a temperature in degrees Fahrenheit and we wanted to convert that to kelvin? We could start to do that by recalling the conversion between the Fahrenheit and Celsius scales.

Say we have a temperature in degrees Fahrenheit. We’ll call it 𝑇 sub F. Well, if we subtract 32 from that value and then multiply the result by five-ninths, we’ll get a temperature in degrees Celsius, which is equivalent. So then, to go from the Fahrenheit to the kelvin scale, we can replace 𝑇 sub C in this equation at the top with five-ninths multiplied by 𝑇 sub F minus 32. That’s because this expression is equal to 𝑇 sub C. So, when we make that substitution, we find that five-ninths multiplied by the quantity a temperature in degrees Fahrenheit minus 32 with 273 added to it is equal to the equivalent temperature in kelvin. Knowing this, we can now convert from a temperature given in degrees Fahrenheit to an equivalent temperature in kelvin.

But what about in the opposite direction, kelvin to degrees Fahrenheit? To do that, we can use this same exact relationship, but we just need to rearrange it a bit. The first step we could take in that direction is to subtract 273 from both sides. When we do this, the negative 273 and the positive 273 on the left cancel one another out. And then, as a next step, we can multiply both sides of the equation by nine divided by five. We choose this particular fraction because nine divided by five multiplied by five divided by nine is equal to one. And then having done that, as a last step, we can add 32 to both sides. Doing this cancels out 32 with negative 32 on the left, giving us this result. Which is now an equation for a temperature in degrees Fahrenheit in terms of one given in kelvin.

Let’s test this equation to see if it agrees with what we already know. The temperature at which water boils on the kelvin scale is 373. So, if we substitute 373 in for 𝑇 sub K, as usual leaving off the units as we do a conversion calculation, then when we subtract 273 from that, the result will be 100. That’s what will remain in the parentheses. If we take 100 and we multiply it by nine divided by five, then the result is 180. And then, if we take 180 and add 32 to it, the result of that is 212. That, our equation says, is the equivalent temperature in degrees Fahrenheit of 373 kelvin, the temperature at which water boils. So, this, indeed, is how we connect the kelvin and the Fahrenheit temperature scales. And we’ve already seen there is a simpler relationship between the kelvin and Celsius scales. Let’s get some practice now with these conversions through a couple of examples.

What is 27 degrees Celsius in kelvin?

Okay, so here we want to convert a temperature in one temperature scale, the Celsius scale, to an equivalent temperature in the kelvin scale. To get started, let’s recall some of the values that these two different scales give to particular temperatures. We’ll start with absolute zero, the temperature at the bottom of any temperature scale. Nothing can be colder than this. And on the kelvin scale, absolute zero is zero kelvin. Meanwhile, on the Celsius scale, it’s negative 273 degrees Celsius. We could say that these are two different expressions for the same temperature, one expressed on the kelvin scale and the other on the Celsius scale. Along with absolute zero, another significant temperature is the temperature at which water freezes. In kelvin, this is 273. Whereas in degrees Celsius, it’s zero.

So, we can see that for both of these temperatures, going from absolute zero to the temperature at which water freezes involves adding 273. This tells us something about how to convert from degrees Celsius into kelvin. We can see that if we take a temperature in degrees Celsius, we’ll call it 𝑇 sub C, then to express that temperature in a different scale, on the kelvin scale, we need to add 273 to it. To see why that is, look at the temperature at which water freezes. We could say that that’s zero degrees Celsius, and we can also say that it’s 273 kelvin. And to go from Celsius to kelvin, we need to add 273.

So then, given a temperature in degrees Celsius, if we add 273 to it, we get the equivalent temperature in kelvin. And this is the relationship we’ll use to answer our question. We want to know what 27 degrees Celsius is in kelvin. So, in place of 𝑇 sub C, we’ll put 27 and we’ll leave the units off, as we normally do when converting between temperature scales. And then to that, we’ll add 273. If we do this, then according to our equation, we’ll get the equivalent temperature in kelvin. We’ve called it 𝑇 sub K. 27 plus 273 is 300. And now, we put on the particular unit of our scale. This shows us that 27 degrees Celsius is equivalent to 300 kelvin.

Let’s look now at a second example.

What is 330 kelvin in degrees Celsius?

Okay, so in this exercise, we want to convert a temperature in the kelvin scale to an equivalent one in the Celsius scale. To do this, we can start by recalling the particular values that these two scales, the kelvin and the Celsius scale, give to describe the temperatures of absolute zero and the temperature at which water freezes. Now, the kelvin scale was designed around absolute zero, so that absolute zero is at zero kelvin. The equivalent temperature on the Celsius scale is negative 273. Then, if we consider water freezing or equivalently ice melting, that happens at 273 kelvin. And then, on the Celsius scale, it happens at zero.

So, on both of these scales, on both the kelvin and the Celsius scale, we add 273 to go from the temperature at absolute zero to the temperature at which water freezes. This tells us that if we have a temperature, in general, in kelvin, we can call it 𝑇 sub K, then if we take that temperature and subtract 273 from it, we’ll get the equivalent temperature in degrees Celsius. So, given a temperature in kelvin, if we take away 273, we’ll get the equivalent temperature in degrees Celsius. And we can test this out using our temperature scale. Over here, we have 273 kelvin, and then if we subtract 273, we get zero, and that’s degrees Celsius. And then an absolute zero, zero kelvin, minus 273 is negative 273 degrees Celsius.

Now, in our exercise, we want to take 330 kelvin and convert that to degrees Celsius. This means, in place of 𝑇 sub K, we’ll write 330, and we’ll leave off the units as we normally do in converting between temperature scales. So, we take our temperature in kelvin and then we subtract 273 from it. And that, our equation says, is the equivalent temperature in degrees Celsius. Well, 330 minus 273 is 57. And it’s at this point, at the end, that we put on our units. They’re degrees Celsius. And we found our answer. 330 kelvin is 57 degrees Celsius.

Let’s summarize now what we’ve learned about the kelvin temperature scale. Starting off, we saw that three of the most common temperature scales are the Fahrenheit, Celsius, and kelvin scales. We saw further that the kelvin is the SI base unit of temperature. In this system then, temperatures are often expressed in kelvin. Further, we saw that there is a temperature called absolute zero, which is the lowest temperature that an object can have. This temperature is the basis for the kelvin scale. Absolute zero is zero kelvin. And then, on the same scale, the temperature at which water freezes is 273 kelvin and the temperature at which water boils is 373 kelvin.

And on the Celsius scale, these equivalent temperatures are negative 273, zero, and 100, respectively. And lastly, we learned conversion formulas between the Celsius and kelvin scales, and the Fahrenheit and kelvin scales. Knowing these equations, we can convert any temperature in any of the three common temperature scales to its equivalent temperature in the other two. This is a summary of the kelvin temperature scale.

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