- #36
George Jones
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Urmi Roy said:2. How many state variables (Voume,pressure,temperature etc.) are needed to specify a thermodynamic system?
Andy Resnick said:Please see, for example,
http://arxiv.org/abs/math-ph/0703061
For a single phase, the 5 variables are pressure/volume, temperature/entropy, and U.
DrDu said:Andy, one counterexample may be sufficient. For an ideal gas, U is a linear function of T only and S can be expressed in terms of T and V (Sackur Tetrode equation). So e.g. T and V are sufficient to specify the state in all respects.
Urmi Roy said:I found something called the two property rule which says that the state of a thermodynamic system in equilibrium can be completely defined by 2 variables.
Urmi Roy, there is an ambiguity in question 2. from your first post. Did you mean:
2. How many state variables (Voume,pressure,temperature etc.) are needed to specify an arbitrary (possibly non-equilibrium) state (at a fixed time) of a thermodynamic system?
If you meant this, then I think the answer is 5, as Andy has said.
Or did you mean
2. How many state variables (Voume,pressure,temperature etc.) are needed to specify an equilibrium state of a thermodynamic system?
If you meant this, then I think the answer is 2, as DrDu and the_house have said. So, I think Andy and DrDu have been answering different questions.
Things are still fuzzy for me, but here is what I think is going on. It takes 5 variables, pressure, volume, temperature, entropy, and U, (in the simple, but general systems we are considering) to pin down an arbitrary state. Since Q = TdS for quasi-static processes, the (hyper)surface on which dU = TdS - PdV holds is the set of all equilibrium states. I think it can be shown that this surface (in our case) is 2-dimensional. To find a specific 2-dimensional manifold of equilibrium states, an equation of state is used. The equation of state together with dU = TdS - PdV is used to generate two Maxwell(-like) relations. The equation of state together with the two Maxwell relations act as three equations of constraint that restrict the 5-dimensional manifold of arbitrary states to the 2-dimensional manifold of equilibrium states.