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Absolute temperature and the kelvin scale

Video transcript
Voiceover: All bodies and systems possess a property called temperature. Most commonly temperature is used to refer to how hot or cold something is, but the real sciency definition of temperature is that it's a measure of the average kinetic energy of the particles in a system. I've got a system and I'm filling it with little individual particles. If we think about this microscopically each little particle in the system is moving in some way whether in rotation or in a straight line, or curving, or by kind of a combination of these means. All of these little particles are moving. The energy of motion is called the kinetic energy. All of these moving particles have kinetic energy. The faster those little particles are moving, the greater their kinetic energy. If each of those little particles in the system has greater kinetic energy, that means the system as a whole has a larger amount of total energy, and we would say that it has a greater temperature because, again, temperature is a measure of the average kinetic energy of those particles. Because knowing the amount of energy in a system can be really useful in chemistry and in physics, we've developed temperature scales to help us quantify or measure the amount of this value, this value of energy. The three scales most widely used are the Kelvin scale, the Celsius scale, and the Fahrenheit scale. For all of these scales I'm going to draw a little thermometer, one for Kelvin. Then we have a thermometer for Celsius, and then another thermometer for the Fahrenheit scale. The two scales used most in the physical sciences are probably the Celsius scale and the Kelvin scale. As a point of comparison here on these thermometers, the freezing point of water occurs at zero degrees Celsius. We have zero degrees Celsius. That's where water freezes. Then the boiling point of water occurs at 100 degrees Celsius. So the boiling point of water occurs at 100 degrees Celsius. That's where water turns into steam. I'm going to write H20 here real quick just so we don't get confused that we're talking about the freezing and boiling point of water. Now when we use the Kelvin scale, we find that water's freezing point is 273.15 Kelvin. Then we find that water boils at 373.15 Kelvin. They differ fundamentally in the zero point. The Celsius and Kelvin scales differ in the zero points that they use, but between water's freezing point, and water's boiling point, we have a span of 100 temperature units for both scales. So although they differ in the zero points that they use. They use the same size unit, or the same magnitude of unit to measure the temperature. Converting then between the two scales only really requires that we make an adjustment for the two different zero points. This is what I mean. If we want to know the temperature in Kelvin, all we need to do is take the temperature in Celsius and add 273.15 degree units to it. If we want to know the temperature in Kelvin for the freezing point of water, we take the temperature in Celsius which would be zero, and we add 273.15 units to it, and that would give us 273.15 Kelvin. Now if we want to flip that, and if we want to find the temperature in Celsius from Kelvin, all we have to do is take the Kelvin figure and subtract 273.15 to it, or subtract 273.15 from it, excuse me. We would see that 373.15 Kelvin minus 273.15 would give us 100 degrees Celsius. Just as another example, let's convert 300 Kelvin to Celsius. To start, since we're looking for Celsius, we'll take that Kelvin value, and we'll subtract 273.15 from it. That's going to give us 26.85 Celsius. So 26.85 degrees Celsius is the same thing as 300 Kelvin. I just want to point out really quickly that I'm only using the degree symbol here for Celsius, and I'm doing that intentionally. We don't need this symbol with Kelvin scale because instead of calling the temperature units degrees, we just call them Kelvin. The only thing we need is an uppercase K. Now converting between the Celsius and Fahrenheit scales is a little bit more complicated. You see in Fahrenheit, water freezes at 32 degrees Fahrenheit, and water boils at 212 degrees Fahrenheit. This give us a span between the freezing point and the boiling point of water of 180 degree units. We're going to need to consider two different adjustments here; one for degree size because the units have a different magnitude, and the same value, or the same span of temperature is 100 units in Celsius and 180 units in Fahrenheit. We're also going to need to account for the two different zero points, zero degrees Celsius for freezing, and 32 degrees Fahrenheit for the freezing point of water. First we can say that 180 degrees Fahrenheit is equal to 100 degrees Celsius. Again, we can say this because both of these magnitudes refer to the same change in total energy. If we write this as a ratio, we have 180 over 100 which just reduces down to nine over five. So the ratio of Fahrenheit to Celsius is nine to five. Now we need to think about the two different zero points. Because 32 degrees Fahrenheit is equal to zero degrees Celsius, we can find the Celsius temperature if we take the temperature in Fahrenheit and we subtract 32 degrees from it. This makes sense because 32 degrees Fahrenheit minus 32 degrees Fahrenheit would give us zero degrees Celsius. Now we just need to apply the unit ratio, so just like any dimensional analysis problem, we need to cancel out the degrees Fahrenheit. If we put the degrees Fahrenheit on the bottom here, so nine degrees Fahrenheit, we can cancel out the Fahrenheit leaving us with just degrees Celsius. To find the temperature in Celsius, we take the temperature in Fahrenheit subtract 32 from it, and multiply it by a ratio of five to nine. Then we can also manipulate this formula if we want to start with Celsius. All we have to do is solve for the temperature in Fahrenheit. To start we would divide both sides by five over nine, or that's the same thing as multiplying by the reciprocal. Then to finish it off, we would just add 32, so plus 32 is equal to the temperature in Fahrenheit. Now if we want to start with temperature in Celsius, we can move to temperature in Fahrenheit, or we could start with temperature in Fahrenheit and move to temperature in Celsius. To practice this let's go from Celsius to Fahrenheit. It turns out that these temperature scales actually cross paths at a temperature which is kind of a fun fact. If we plug in negative 40, let's go from negative 40 degrees Celsius to Fahrenheit. We'll find that TF is equal to negative 40 times nine-fifths plus 32. We can reduce this term here, so five and negative forty reduces to negative eight. So negative eight times nine plus 32. That's negative 72 plus 32. So the temperature in Fahrenheit would equal negative 40 as well. So negative 40 degrees Celsius is the same thing as saying negative 40 degrees Fahrenheit. That's kind of just a fun fact. And another observation from this little factoid is that Celsius and Fahrenheit scales can both have negative or positive values. We see that both can be at negative 40. These can both have negative values. That's actually a point where they differ from the Kelvin scale. The Kelvin scale can only have a positive value. It turns out that the absolute coldest temperature is zero Kelvin. So zero Kelvin is absolute zero. The reason we can't get any colder is that at this point, no particles would have any kinetic energy. That means no motion at all. We said that temperature is a measure of the kinetic energy, and the coldest that you can get is no kinetic energy whatsoever. It turns out that the laws of physics specifically the uncertainty principle just don't allow for this. We can get close like within a billionth of a Kelvin, but we can't get all the way there. Because Kelvin scale always has a positive value, it becomes a little handier in various formulas, so to use as the standard, the SI unit for temperature. I'll show you in future videos why absolute zero happens at negative 273.15 degrees Celsius, but I'm starting to run out of time in this one so I'm going to have to save it for later. I'll talk about that with Charles's Law in the future.