In thermodynamics I can e.g. compute the properties of ideal gases with certain
ID: 1373971 • Letter: I
Question
In thermodynamics I can e.g. compute the properties of ideal gases with certain energies U1,U2 in boxes with certain volumes V1 and V2. Say I have two such boxes and they have some specific parameter values, like say I know their temperatures T1,T2. Now I put them together, the gases can interact and I thereby construct a new box with volume V1+V2 and the energy is U1+U2. Using the laws of thermodynamics, I can compute everything else again now. Say I find a new temperature Tnew.
One says that the temperatures of the gases in the systems changed by putting the boxes together. However, on the computational side what I did was just considering a system of new specifications. To get the new result, I didn't have to enter the real world staring conditions except for the variables which also were necessary to compute their respecive properties - effectively, the theory didn't have to tell me how the system changed, just what the restrictions are - and I basically entered into a new system with these values. For example, it's not relevant which gas had with specifications before. I just did a little trivial algebra and computed what has to be. When then talk about a change of entropy and how the gas behaves, but that seems to be only decorative.
If I say that the second law of thermodynamics tells me that heat flows from a system with high temperatures to a system of low temperature I'll be able to derive rules for the entropy say, how the combined system has to look like if I state their variables and insist on extensivity of certain variables and so on - but it's not about change in the sense that I compute how the system developes from one point to the other in details. Rather I just compute how the end configuration has to be.
My question is
Is the starting configuration of a thermodynamics system ever relavant?
And secondly,
In thermodynamics, if I compute "the change a system" in the sense of the above example, do I always induce the necessarity for doing such a thing by stating "now we bring system one and system two in contact"?
Explanation / Answer
(i) Yes, the starting configuration is relevant. It determines the later state of the thermodynamic system.
(ii) Changes in a system happen automatically whenever temperature, pressure, or chemical potential are not uniform in the system. (The gradients of the corresponding fields generate forces changing the sytem, until equilibrium = a maximaum entropy state) is achieved.
''Bringing two systems into contact'' is only a particular way to prepare initial conditions of very simple form.
(iii) To compute how entropy changes (this is the subject of nonequilibrium thermodynamics), you need a more specific model than just generakities about thermodynamics.
For example, the nonequilibrium thermodynamics of water is given by the Navier-Stokes equations. In addition to conservation of mass, energy, momentum, and angular momentum, one can derive from the equations a formula for the entropy production, whichis nonnegative at each point, and is a term in the differential equation for entropy that implies that entropy increases globally in an isolated system.