A box is separated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured, and equilibrium is eventually attained. Assume that the volume of the box is large enough for each gas to undergo a free expansion and not change temperature. (a) On average, how many molecules of each type will there be in either half of the box?

Video transcript

everyone in this problem. We have two identical cylinders, K and B. That are connected by a short tube with a valve cylinder A contains and the molecules of helium And cylinder B contains three and molecules of our body. The valve is initially closed. Both gasses are at the same temperature. After the valve is opened, the helium and argon gasses will expand icy thermally and were asked to determine the average number of molecules of helium and argon present in each cylinder. All right, So let's think about this. Okay, we have ice thermal expansion and we have two identical cylinders. So once that valve is opened and the gasses expand, we're going to end up with an equal probability for the gasses to be in either cylinder. Okay, so there's an equal probability that they're going to be an either cylinder. Then on average, we're just going to get half of helium in container a half of it and be half in. And same with argon right half and container a half in container be on average. So, what that means? We have n molecules or helium And we have three n argon. We have three n molecules. And we're going to expect on average because they have an equal probability to be either cylinder that we're gonna get half. Okay, so half of the healing molecules will be n over two, Half of the argon molecules will be three and over two. And so we're going to have answers. See we would expect on average, and over two molecules of helium and three and over two molecules of argon and cylinder A and the exact same in cylinder B. Okay, I hope this video helped. Thanks everyone for watching. See you in the next one.