Great! Good luck, and please do let me know how you do. My main goal is to help people learn thermo (and other PChem topics), but passing an exam is a nice side effect
Why do we assume its constant temp and pressure in beginning but then its different in the end the derivation is based on the fact that its constant right proffesor??
No, not quite. This is a fairly subtle point in the derivation. When T and P are constant, then dG = Σᵢ μᵢ dnᵢ. But when T and P are not constant, then dG is something different: either dG = Σᵢ μᵢ dnᵢ - S dT + V dP or dG = Σᵢ μᵢ dnᵢ + Σᵢ dμᵢ nᵢ. These two results (from which the Gibbs-Duhem equation follows) are true even when T and P are not constant.
Wonderful 👏👏👏👏 amazing 👏👏👏 words are unable to describe this explanation 👏 it's the 4th time I've watched this video . Every time I watch, I learn something new. Beyond the words👏👏👏🌹🌹🌹
The derivation has a flaw: in the first part of it, he considers T and p constant, so the sum of mols x d. potentials = 0 only holds in this condition. But it later applied it to dG in the general case. This proof only is valid por the Gibbs-Duhem equation with T and p constant.
Hi again hehe! Why can we equate both of the expressions for dG? One came by taking the derivative of G = ∑𝜇𝑖n𝑖 provided that T and P are constant. But dg = -SdT + Vdp + ∑𝜇𝑖𝑑𝑁𝑖 doesn't need to be at T,P cte. So why is it allowed two equate two expressions that are defined for different conditions: one under cte T and P and the other doesn't require T, P to be constant . Your videos are really helpful. Thanks! Regards from Spain!
Good question. It's actually the case that G = Σᵢ μᵢNᵢ even when T and P are not constant. That's not proven in this video, but it is true. One way to understand this: if you know that U = TS - PV + Σᵢ μᵢNᵢ , and G = U - TS + PV, then G = Σᵢ μᵢNᵢ .
@@gemacabero6482 The proof can be found on Wikipedia, but it should go as follows: The natural variables of U are all extensive properties: S, V and N. As U is extensive as well we have: U(λS, λV, λN) = λU. So U is a first order homogeneous function. An example of such a function, ignoring the physical meaning, is U = S*N/V. For the Euler theorem we have U = S ∂U/∂S + V ∂U/∂V + N ∂U/∂N = S ∂U/∂S + V ∂U/∂V + Nμ. We know from the fundamental relationship for U (dU = TdS - pdV + μdN) that ∂U/∂S = T and ∂U/∂V = -p. Substituting in the equation above: U = TS - PV + Nμ The rest follows as Steven was saying.
It may look easy, but the simplicity holds some pretty deep truths. We usually use it as a link in thermo derivations, rather than to solve numerical problems. So keep your eye on what it **means**, and hopefully you won't be confused when it reappears in later material.
I´m from germany, but although there´s the language barrier, It´s way better explained than in my lectures ^^ Thank you!
I'm glad I could help. Sorry my German is not better. :-)
Thank you so much for this video! My prof essentially hand-waved this topic and left us to study it on our own, so this was such a big help.
This guy is an excellent teacher. Bravo
Sir you are helping a lot for my upcoming Thermodynamics exam, if I manage to pass it I will come back here and pay my thanks again!
Great! Good luck, and please do let me know how you do. My main goal is to help people learn thermo (and other PChem topics), but passing an exam is a nice side effect
Why do we assume its constant temp and pressure in beginning but then its different in the end the derivation is based on the fact that its constant right proffesor??
No, not quite. This is a fairly subtle point in the derivation.
When T and P are constant, then dG = Σᵢ μᵢ dnᵢ. But when T and P are not constant, then dG is something different: either dG = Σᵢ μᵢ dnᵢ - S dT + V dP or dG = Σᵢ μᵢ dnᵢ + Σᵢ dμᵢ nᵢ. These two results (from which the Gibbs-Duhem equation follows) are true even when T and P are not constant.
Wonderful 👏👏👏👏 amazing 👏👏👏 words are unable to describe this explanation 👏 it's the 4th time I've watched this video . Every time I watch, I learn something new. Beyond the words👏👏👏🌹🌹🌹
Thanks a lot, your videos helped me a lot
You're welcome, I'm glad to hear it
The derivation has a flaw: in the first part of it, he considers T and p constant, so the sum of mols x d. potentials = 0 only holds in this condition. But it later applied it to dG in the general case. This proof only is valid por the Gibbs-Duhem equation with T and p constant.
Hi again hehe! Why can we equate both of the expressions for dG? One came by taking the derivative of G = ∑𝜇𝑖n𝑖 provided that T and P are constant. But dg = -SdT + Vdp + ∑𝜇𝑖𝑑𝑁𝑖 doesn't need to be at T,P cte. So why is it allowed two equate two expressions that are defined for different conditions: one under cte T and P and the other doesn't require T, P to be constant . Your videos are really helpful. Thanks! Regards from Spain!
Good question.
It's actually the case that G = Σᵢ μᵢNᵢ even when T and P are not constant. That's not proven in this video, but it is true.
One way to understand this: if you know that U = TS - PV + Σᵢ μᵢNᵢ , and G = U - TS + PV, then G = Σᵢ μᵢNᵢ .
@@PhysicalChemistry Thank you!
@@gemacabero6482 The proof can be found on Wikipedia, but it should go as follows:
The natural variables of U are all extensive properties: S, V and N. As U is extensive as well we have:
U(λS, λV, λN) = λU.
So U is a first order homogeneous function. An example of such a function, ignoring the physical meaning, is U = S*N/V. For the Euler theorem we have
U = S ∂U/∂S + V ∂U/∂V + N ∂U/∂N = S ∂U/∂S + V ∂U/∂V + Nμ.
We know from the fundamental relationship for U (dU = TdS - pdV + μdN) that
∂U/∂S = T and ∂U/∂V = -p.
Substituting in the equation above:
U = TS - PV + Nμ
The rest follows as Steven was saying.
Super clear video, thanks a lot!
Great, glad it was clear
God bless you!
this looks so easy, thank you!
It may look easy, but the simplicity holds some pretty deep truths. We usually use it as a link in thermo derivations, rather than to solve numerical problems. So keep your eye on what it **means**, and hopefully you won't be confused when it reappears in later material.
Excellent
Thanks
Sir how are you writing in reverse?
I'm not! The image gets reversed digitally. More info: czcams.com/video/YmvJVkyJbLc/video.html
@@PhysicalChemistry didn't think of that😂
Thank you!
You're welcome!
subbed, ty !
Great, thanks!