Hey, guys. So, in earlier videos, we talked about temperature. In this video, I'm going to show you a related idea of thermodynamics called heat and the role that heat plays in changing the temperature of an object. We're also going to talk about something called the specific heat, and I'm going to show you a very straightforward equation that you absolutely need to know. Let's check this out here. So, before I go any further, I want to talk about heat and temperature. These are two words that we use sort of interchangeably in everyday life. So we say things like, "I can't stand the heat. It's unbearable." What we actually mean is that we can't stand the temperature of wherever we are. But these things have very specific definitions in physics that you need to know. Let's talk about temperature. We've actually already talked about temperature before, given by the letter t. It's kind of just a measure of the kinetic energy of the molecules that make up a substance, kind of a measure of how hot or cold something is or feels. So the idea here is I have these two substances, and if these molecules are moving faster, they're going faster, they have more kinetic energy, and therefore the temperature is higher, like 20 degrees Celsius versus 10 for a colder object. So that's temperature. Heat, on the other hand, is a little bit different. Heat is given by the letter q, and what heat is, it's a transfer of energy. It's a transfer of energy between two materials that is caused by a difference in temperature. So here's the idea. These two substances over here both have their own individual temperatures. One's at 20 and then one is at 10. So those temperatures are different. And so because of that difference in temperature, it's going to cause energy to be transferred between these two materials. That's what heat is. So the analogy that I like to use is that temperature is like kinetic energy or just energy in general. An object can have energy, and heat on the other hand is kind of like work. An object can't have work. Work is something that is transferred or done between two objects, and that's exactly what heat is. It’s a transfer that's caused by a temperature difference. Now, what's important about heat is that it has a direction. Heat always flows from hotter to colder substances. So this heat that gets transferred, this q, has a direction. It always flows from hotter to colder. It basically always goes from high to low temperature just like a lot of things in physics go from sort of high to low. It's the same idea here. And basically, they're going to continue exchanging this energy, heat is going to continue flowing from the hotter to the colder until they reach what's called thermal equilibrium. So you can imagine that these two things, one's at 20, one is at 10, when you mix them together, eventually they'll reach an equilibrium temperature, that is 15 degrees Celsius, just making that up here. And then what happens is that when they reach this equilibrium, the q is equal to 0. There's no more heat transfer anymore.

Alright. So now that we know what heat is, let's talk more specifically about what heat does, because you're going to need to know the equation that relates this heat with the temperature change. So when a material absorbs heat, like plus q, or loses heat, minus q, it's going to change temperature. So the idea here is that if you took water and heated it from 0 to 10 degrees Celsius, you had to put in some heat in order to do that, in order to increase its temperature. But you can also change an object’s phase. Now we're only going to talk about temperature in this video. We’re going to talk about phase in a later one. All you need to know for now is that phase is kind of like solids, liquids, and gases. These are like the states of matter. And if you input energy, you can also change the phase of an object. So for example, if you stuck ice in a microwave, you would change the temperature of that ice, but also at a certain point, you're going to melt the ice into water. It's going to change from solid to liquid. Now we're going to talk specifically about the change in temperature equation over here. The equation for this is: q = m c ∆ t . This is sometimes referred to as the MCAT equation because if you imagine that this delta sign sort of grows legs, it kind of looks like the word mcat. Right? So the m is the mass of the object, the delta t is the change in the temperature, and this variable, this letter c here, is something called the specific heat of the material. Here are the units for the specific heat. And one way you can think about the specific heat is it's kind of like a measure of thermal inertia. Remember that inertia is like a resistance to change. This thermal inertia is a resistance to changes in temperature. You can think about it as how hard it is to change temperature from any heat that is gained or lost. If you ever need this c variable, there's a constant, it's going to be given to you, because it basically just has to do with the material that is involved. And the idea here is that if the c is higher, for higher values of c, it's more difficult to change temperature for the same amount of heat. Basically, if your c is higher, then you need more q in order to change an object’s temperature. Alright? So here's actually some examples. I've actually got some substances down here with some pretty, some common ones with their specific heats. So, for example, copper, iron, and lead all have specific heats that are sort of in the 100, but ice and water have specific heats that are in the 1,000. So they’re much higher than metals. This kind of makes sense. If you take an iron skillet and you put it on the stove, it's going to heat up very quickly, but then the water that you put into the pot or something like that in order to boil it, it takes a long time for it to change temperature. Alright? So let's go ahead and get to our example here. So we’ve got, the heat required to reach the temperature of 50 grams of water from 40 to 55. So we've got the mass, which is equal to 0.05, and we’ve got the, specific heat. Let’s see. Actually, we're going from a temperature that's t initial equals 40 degrees into a t final of 55 degrees Celsius. We also know that we're dealing with water, so the specific heat of water that we're going to use, this is CW, I'm just going to call this, is 4186, and that’s the, these are the units right here just in case you need them. So with that being said, how much heat do we need? Well, this is just q equals mc times delta T. So we have m, we have the c for water, and all we need to do is just figure out the change in the temperature. So we were told that we’re going from 40 over to 55 degrees Celsius. So the idea here is, does delta t actually equal 15? And the answer is yes because remember delta t in Celsius is the same thing as delta t in Kelvin. So if you’re calculating the deltas, it actually doesn't matter. If you were to convert these things to Kelvin, the difference would still be 15. So it actually doesn't matter which one you plug in.