Hey, everybody. So let's take a look at our problems. We have a car that's driving along the road. It's going to suddenly slam on the brakes, and we want to calculate what's the change in entropy of the air. So in other words, what we want to calculate here is delta S, and I want to say delta S for the air. But before we get started, I want to sort of draw out what's going on here. Right? So we've got this little road, and I'm going to draw this little car like this. Don't make fun of my car drawings. Like that. And then what happens is it's chugging along initially at some initial speed, which is 20 meters per second. Then what happens is over some time, it's going to slam to a stop. So eventually what happens is that V final is going to be 0. Alright? So what's going on here? If you want to calculate the change in the entropy, we're going to have to use the change entropy equation. Now remember, we can only use this equation Q over T as long as the temperature remains constant, but it does because we're told in this problem that when you slam on the brakes, the air, which is, like, so massive and large, remains at a constant temperature of 20 degrees Celsius. So what happens is if you add a little bit of heat to it, the air is obviously so massive that it doesn't really change temperature. So we have delta S for the air is the heat that's added to the air divided by that temperature. Right? So we have what that temperature is. So the question here is, well, how much heat is actually added to the air? We don't have an equation for this. Right? We can't use like Q equals MCΔT or something like that because we don't have the mass of the air, we don't have the specific heat. So what's really going on? Well, what happens here is that we have to realize that this initial velocity for the car means that this car has some kinetic energy. So in other words, this kinetic energy, I'm going to say K_initial is equal to 12mv02. Squared. Actually, I'll call this K_zero. So I'll call this K_zero. And eventually what happens is that when you slow to a stop, right, you slam on the brakes, eventually when you get to this point here your K_final is equal to 0. So in other words, you had some kinetic energy and then you lost it because you slammed on the brakes. So then where did all of this energy go? Remember that energy can only change forms. It can't be created or destroyed. It doesn't go to potential energy because it's still staying at the same height. So basically what happens here is that all of the K that gets transferred basically goes into friction. It goes into the friction of the brakes and that gets dissipated as heat. Remember, friction, when you rub something, it's really just heat transfer. So what happens here is that the delta K, the change in the kinetic energy, really just becomes Q. It becomes the Q that gets given off to the air. Alright? So that's what's going on. So basically, what we can do here is we can say, well, the Q_air really comes from the change in the kinetic energy. Now really what happens is this change is really just the 12mv02 because the K_final is 0. So we don't have to do final minus initial. So this really just becomes one half, and this is going to be mv02. We have the mass of the car and the initial speed, so then we can go ahead and do that. So we're going to have one half of the mass, which is 1500 times the initial velocity, which is 20 squared. So now you divide that by the initial temperature. Now the temperature is 20 degrees Celsius, but we have to convert that to Kelvin. So this just becomes 293 Kelvin, and that's what we plug into our denominator here. So if you work this out, what you're going to get is that the change in the entropy for the air is equal to, 1.02 times 10 to the third, and this is going to be joules per Kelvin. Alright? So that's how much entropy gets sort of dissipated. That's how much energy you've now dissipated. The energy is a little bit more random and therefore the entropy of the universe increases. Alright. So that's it for this one guys. Let me know if you have any questions.
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Entropy and the Second Law of Thermodynamics
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