JEE Main Physics Thermodynamics #5 Kinetic Theory of Gases

welcome to electron line the next problem from the je main test deals with thermodynamics and this one here deals with kinetic theory of gases and they give you four statements and they ask you the following on the basis of on the basis on the kinetic theory of gases the gas exerts pressure because the molecules and then these four statements should be able to finish that sentence either they suffer change in momentum they can continue to stick to the walls they continuously lose their energy or they are attracted by the walls which of these four statements is true so we need to understand more about what they mean by the kinetic theory of gases and so if you know that the answer will become apparent very quickly if you don't know the kinetic theory of gases you might be able to figure things out but let's talk about the cadet theory of gases so what they are saying in that theory is that of course is a whole bunch of molecules and travel in all kinds of different directions but you could simplify things by assuming that because each of the velocities will have the three components in the x y and z direction you can assume that one third of all molecules travel in one direction one third the molecules travel in a second direction and one third of all the molecules travel in the third direction x y and z directions of course and we can even make it more simplistic let's have all the molecules going back and forth in just one direction to simplify it so what exerts pressure at the side of the wall or the wall of the container well what creates pressure is a molecule bumping into the wall and then going back in the other direction at the same velocity so we have a plus v velocity here minus v velocity here so that the delta v is equal to two times the um the magnitude of delta v is 2 times v of course that's the way we should look at it and then we can also think about impulse we know that the impulse is equal to force times delta t and we know that pressure is equal to force divided by area so that force is equal to pressure times area so that the impulse times delta t or finally when we put it all together oh pressure that's not a good looking a here a there we go and then when we put all together we can say that pressure is equal to the impulse divided by the area divided by delta t and the impulse of course would be m times the change in velocity divided by area my a's look terrible here today times delta t and of course that would be equal to m times 2 v i'm missing my 2 here really messing up today there we go 2v divided by a times delta t so it all is this what means what this means is that the pressure is created by the change in velocity and then how often does this occur and then on any one wall the time that it takes between collisions that's the total amount of time that lapses so when it travels from here to there that's your delta t once you know its velocity and you know the length of travel you can find your delta t so essentially the pressure is equal to the mass times twice the velocity times the area times the time it takes to go from here to here and back that's what we mean by the kinetic theory of gases in a nutshell so once you know that you look at the four answers and it says that the molecules suffer a change in momentum when they impinge on the walls of the container that's exactly what is happening and so from that we can say answer a appears to be correct but just to be on the sure side let's read the other three answers to make sure that none of those are correct continuously stick to the walls of the container well if they stick the walls in a container then how would they get unstuck and how long would they be stuck so that doesn't seem like a reasonable explanation how about the next one continuously lose their energy until too many either until they reach the wall that means the molecule will be traveling would be slowing down slowing down and when it reaches the wall it speeds up again that doesn't seem to make sense there's no reason for the molecule to be slowing down so that seems not to be a good solution and finally they're attracted by the walls of the container well if that was the case then they would move faster faster to get close to a wall they move slower as they get away from a wall and then since they're attracted would they be caused to stick to the wall would they then come back at a slower velocity again it doesn't appear like that would

be the case and all the molecules would constantly be changing velocity throughout and that also doesn't seem to be the case so those are the three answers are not good answers this one definitely is the one that meets the criteria for the kinetic theory of gases and again i spend a lot of time explaining it but this is something that you should immediately think about kinetic theory of gases ha that's about the molecules going back and forth they strike the wall the pressure is created by the change in momentum therefore answer a must be correct and so that could be a 15 second question after you read it and move on to the next one and that is how it's done