I don't... but I was anyway hoping for a more general derivation of the relation, since I need it in the context of cosmology, were the gases can be highly relativistic. Or maybe this formula would also apply in that case?
Thanks, this part was clear to me. But in the end, it all boils down to the statement that at equilibrium, ##\sum_{i} \mu_{i} dn_{i} = 0##, but I don't really see the justification for this. Textbooks seem to go in circles, "proving" this statement with the minimization of ##G##, even though...
Yeah, I was also thinking the same. But then I'm not sure how to derive the relation between the chemical potentials ##(\mu_A + \mu_B = \mu_C + \mu_D)## in a reaction ##A+B \to C+D##
Thanks, indeed I had seen this equation 10.2 (unfortunately, the other pages you mentioned are very different in my edition). My issue is, the authors assume both this equation 10.2 ##(d ( nG ) = ( nV ) dP − ( nS ) dT + \sum_{i} μ_{i} dn_{i})## and equation 6.7 ##(d ( nG ) = − nS dT + nV dP)##...
Oh, sorry! I meant the section titled "EQUILIBRIUM AND PHASE STABILITY" in chapter 12. In chapter 10, I also referred to the section 10.2 entitled "THE CHEMICAL POTENTIAL AND EQUILIBRIUM", where the authors also state that ##dG = − S dT + V dP## for the system, because it's closed, even though...
I don't think the grand potential comes into play here. I'm talking about systems of constant pressure and temperature, which are also closed in the sense that no matter can come in or out, but where chemical reactions can occur, such that the relative amounts of each chemical component can vary.
Thanks for your reply! I've checked out the reference, unfortunately it's still not clear to me.
Specifically, in Section 12.4, they use the following form of the first law:
##dU = dQ + dW = dQ − PdV##
They have also used this form in Chapter 10, to derive the relation between the chemical...
I have a rather basic question regarding the chemical potential (##\mu##) in thermodynamics and its relation to the Gibbs free energy (##G##). All thermodynamics textbooks I've looked at (Landau & Lifshitz, Kittel...) derive the fact that, at constant temperature ##T## and pressure ##p##, the...
Hi everyone!
I'm going through Peskin & Schroeder's Chapter 19 (Perturbation Theory Anomalies) and it seems to be that equation 19.74 in page 666 has a minus sign missing on the RHS. Namely, I think the correct equation should read
\begin{align}
(i\not\!\! D)^2 = -D^2 -...