- #1
nonequilibrium
- 1,439
- 2
dE = TdS - PdV, or equivalently [itex]\Delta E = \int T \mathrm d S - \int P \mathrm d V[/itex]
In general this is said to be derivable in the reversible case, however since S and V are state variables, it's also true for the irreversible case.
But it can't be true for any irreversible case, since the formula only makes sense if at each moment T and P are homogeneous: only one value for each for the whole system (although it may vary in time). In most irreversible processes, T and P are definitely not homogeneous (it actually seems kind of characteristic of irreversibility that it includes inhomogeneity of the intensive parameters).
So the fundamental thermodynamic relation is true for irreversible cases in case T and P stay homogeneous in their evolution in time. But how many cases are there of this? I suppose I'm looking for examples. (If one is not scared of the word quasi-static, I suppose (?) I'm looking for irreversible, quasi-static processes, although I'm not yet 100% sure of this characterisation, so comments on this are also welcome.)
In general this is said to be derivable in the reversible case, however since S and V are state variables, it's also true for the irreversible case.
But it can't be true for any irreversible case, since the formula only makes sense if at each moment T and P are homogeneous: only one value for each for the whole system (although it may vary in time). In most irreversible processes, T and P are definitely not homogeneous (it actually seems kind of characteristic of irreversibility that it includes inhomogeneity of the intensive parameters).
So the fundamental thermodynamic relation is true for irreversible cases in case T and P stay homogeneous in their evolution in time. But how many cases are there of this? I suppose I'm looking for examples. (If one is not scared of the word quasi-static, I suppose (?) I'm looking for irreversible, quasi-static processes, although I'm not yet 100% sure of this characterisation, so comments on this are also welcome.)