Hi.
Btw: I haven't studied statistical physics yet, but I have studied the introductory course on thermodynamics.
I've recently been reading Howard Reiss's book on thermodynamics (it's from the 60s) in trying to understand some concepts more deeply than before. This is quite a simple question, really, but it bothers me.
Ok. So classical [itex](P,T,V)[/itex]-systems have six thermodynamical variables (for a single compound, at least): [itex]P,T,V,N,S,μ[/itex] (four if you won't have a chemical reaction and have amount of your substance). But this type of system only has four (two) independent variables, for
-the state equation of the form [itex]f(P,T,V,N,μ) = 0[/itex]
-second law of thermodynamics of the form [itex]g(S,T) = 0[/itex]
restrict these variables from being "just anything" in regard to each other. So it would feel natural to say that the state equation and 2nd law are constraints for these variables.
However, Reiss writes that it is a general principle that adding a constraint adds to independent variables, and lifting a constraint decreases the amount of independent variables. He motivates this with an example of a gas mixture of water vapour, oxygen and hydrogen. He thinks of "not having a catalyst" as a constraint for the reaction. This seems rational - adding the catalyst makes the reaction able to happen (in shorter timescales).
Also in this context the idea that adding a constraint adds to the independent variables seems plausible: if you've restricted the behavior of your system, by changing one of its variables it isn't clear anymore that all the other variables would "change accordingly", right?
So what am I thinking wrong? How should I undestand state equation & the second law then, decreasing the amount of independent variables. And moreover how should I undestand a thermodynamical constraint, then?
1) I haven't understood "constraint" right?
2) Every substance obeys some kind of state equation and the 2nd law, so seeing them as constraints is sensible.
3) Other?
Btw: I haven't studied statistical physics yet, but I have studied the introductory course on thermodynamics.
I've recently been reading Howard Reiss's book on thermodynamics (it's from the 60s) in trying to understand some concepts more deeply than before. This is quite a simple question, really, but it bothers me.
Ok. So classical [itex](P,T,V)[/itex]-systems have six thermodynamical variables (for a single compound, at least): [itex]P,T,V,N,S,μ[/itex] (four if you won't have a chemical reaction and have amount of your substance). But this type of system only has four (two) independent variables, for
-the state equation of the form [itex]f(P,T,V,N,μ) = 0[/itex]
-second law of thermodynamics of the form [itex]g(S,T) = 0[/itex]
restrict these variables from being "just anything" in regard to each other. So it would feel natural to say that the state equation and 2nd law are constraints for these variables.
However, Reiss writes that it is a general principle that adding a constraint adds to independent variables, and lifting a constraint decreases the amount of independent variables. He motivates this with an example of a gas mixture of water vapour, oxygen and hydrogen. He thinks of "not having a catalyst" as a constraint for the reaction. This seems rational - adding the catalyst makes the reaction able to happen (in shorter timescales).
Also in this context the idea that adding a constraint adds to the independent variables seems plausible: if you've restricted the behavior of your system, by changing one of its variables it isn't clear anymore that all the other variables would "change accordingly", right?
So what am I thinking wrong? How should I undestand state equation & the second law then, decreasing the amount of independent variables. And moreover how should I undestand a thermodynamical constraint, then?
1) I haven't understood "constraint" right?
2) Every substance obeys some kind of state equation and the 2nd law, so seeing them as constraints is sensible.
3) Other?