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# Proof: S (or entropy) is a valid state variable

Proof that S (or entropy) is a valid state variable. Created by Sal Khan.

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• I got kind of lost when he started using the integrals, could someone explain what he was trying to prove and how he proved it in simpler terms?
• The integral was just the mathematical way to write the heat, Q, in terms of the volume, V, because that's what he had the proof in terms of from the last video. He couldn't prove that Q1/T1 + Q2/T2 = 0, because he doesn't know what Q1 and Q2 are, but he knows for an isothermal (constant temperature) process that the heat, Q, is equal to the integral of pressure, P, over the change in volume, V. So then he ends up with delta(S) equaling something in terms of volumes, which, form the previous video, he can then use to show that the change in S is equal to zero.
• what is state variable and state function?
• A state variable means it will always be the same AT THAT POINT. So if you choose P1 and V1 as your point for a certain system of ideal gas, no matter how you change P and V, when you get back to P1 and V1, the U will be the same as it was at the beginning (U1).

Think if it this way: On a mountain top, there are always the same Latitude and Longitude, not matter if you hike straight up, or cycle around the mountain, or parachute in. Those coordinates DEFINE your location on the mountain top. Is "tiredness" or "effort" a variable that is always the same for someone on top of the mountain? No. If you crawled up the mountain, you would be more tired than the person next to you who parachuted in. Is your elevation a state variable for a mountain top? Yes. Is your thirstiness? No.

Likewise P, V, T, S, and U are always the same at the same point on a PV diagram, no matter what wacky path gets you to that point. But the amount of W or Q needed depends heavily on what path you took to that PV point (iso-volume is no work, etc).
• It's often emphasized how important it is that the process is reversible. I think I have an idea of what reversible and irreversible processes are, but I can't seem to understand why so many things apply to reversible processes only. Could someone explain that?
• Because reversible processes are ideal, and simplifications of real world problems. In the real world we would have to account for changes in kinetic and potential energy along with friction (and more). That would make these problems much more difficult to solve! So reversible is just an assumption created to make the problems more simple in an introductory course and that's why everything seems to apply just to reversible processes in these videos.
• Has entropy been proven?
• well yes, entropy has been proven. It is part of the second "law" of thermodynamics... laws are rigorously tested and have not been disproven since formulated
(1 vote)
• why dont u take Q2 negetive?wouldn't it mean Q2=-p.del(V)
• Q2 is negative, he is just including the negative inside the variable, because in the end, it doesn't matter after the integral is taken and the result is in terms of volume and temperature only.
• Around Sal says that in the second isothermic process (from C to D) you take away less heat than you needed to add in the first isothermic process (from A to B). Can anyone please help clarify why this is the case and why the heat added and taken are not the same?
• The second isotherm is at a lower temperature and pressure, so it takes less work to compress it, and therefore less heat has to leave the system after the compression to keep the system at the same temperature (on that same lower isotherm).
• I have no idea what's going on, as to be expected. I don't have the background. I am watching these videos, so that when I do take Chemistry, I will have heard the terms before. I know you guys are all taking Chem. now, tell me, will my strategy work?
(1 vote)
• Well, I am taking Chemistry for sure.
Actually Sal hasn't covered chemistry that well. It might be better for you leave this for a while, if you are not understanding. You can always come back later
Get started with calculus. Start from basic limits, and then work your way up. He's explained calculus better than chemistry. Both of them are very important, calculus more so. Ask questions regarding what you don't get. You will get answers. Don't think calculus is too hard. Don't ever give up on it.
here, watch this videos of this person twice your age - http://www.khanacademy.org/stories/bruce
If he can do it, then why can' you. If you don't get something, then try searching for it on the internet. For chemistry, you can go to academicearth.org and listen to the various lectures. You won't get points for it, but atleast you'll get a better understanding.