### 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, then no 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.