Is Enthalpy Always Conserved in Different Expansion Paths?

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Discussion Overview

The discussion centers around the behavior of enthalpy during gas expansion along different paths, specifically comparing a reversible expansion at constant temperature with an irreversible free expansion into a vacuum. Participants explore the implications of enthalpy as a state function and the conditions under which enthalpy changes occur.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that for the reversible path A, the enthalpy change is equal to the heat added to the system, while for the irreversible path B, they claim the enthalpy change is zero.
  • Another participant questions the assumption that work done (w) is zero for the irreversible expansion, suggesting that full expansion into a vacuum implies different conditions that need to be accounted for.
  • A participant clarifies that the volumes for both paths are assumed to be the same, indicating that both paths reach the same final state.
  • There is a discussion about the nature of state variables, with one participant emphasizing that at any state, there is a unique value for each state variable, which is relevant for comparing enthalpies.
  • One participant refers to the concept of free expansion, stating that it involves zero work done, which they believe supports their argument regarding enthalpy change.
  • Another participant mentions the local variations in pressure and volume during free expansion, referencing external sources to support their points about thermodynamic parameters.
  • One participant expresses confusion about the differing enthalpy changes between the two paths despite starting and ending at the same state, questioning the independence of enthalpy from the path taken.
  • A later reply introduces the concept of Joule's experiment as potentially relevant to the discussion, suggesting that it may provide additional context for the questions raised.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of enthalpy as a state function in the context of different expansion paths. Multiple competing views remain regarding the work done during the irreversible expansion and the resulting enthalpy changes.

Contextual Notes

Participants highlight limitations in their assumptions about work done during the irreversible expansion and the definitions of state variables, which may affect their conclusions about enthalpy changes.

flamcsd
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Consider gas here as idea gas.

The gas expands from state 1: P1, V1 and T1 to state 2: P2, V2, and T1 using two different paths:

Path A: reversible expansion at constant T
Path B: irreversible expansion by releasing the gas to a vacuum to achieve V2 at adiabatic condition.

Thing I confuse: consider that enthalpy as a state function: H1 to H2 from state 1 to state 2.

for reversible path A:　dU = q + w. dU = 0. so q=-w. The system needs some q from surrounding to perform w. and dH = q. H2 = H1 + dH = H1 + q.

but for Path B: w=0, q=0, dU=0. dH=0. So, H2 = H1.

Why? my question is enthalpy can't be same for path B, because enthalpy is a state function which is independent from its path.
 
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How did you arrive at w = 0 for the second expansion?

Don't forget that full expansion into a vacuum implies that P2 = 0 & V2 = ∞

The work done is pv work which is the area in the pv indicator diagram shown.

Between some point C at P3, V3 (say 1 atmosphere) and vacuum (unattainable) the work is shown by the hatched diagram.

If you take it all the way to infinity as shown the work is the area under the whole graph.

You need to integrate an equation of state for the gas to obtain this figure.
 

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Thanks for your reply

the V2 in path B is assumed equal to V2 in path A. therefore, Path B and Path A could both reach a same state, P2, V2, and T1.

the vacuum part is V2-V1, it's like lift a barrier and let the gas go to extra V2-V1 part and reach V2. I don't want V2 go infinite.
 
The point of state variables is that at any state there is one and only one value available to each state variable.

So to compare enthapies, start and end points have to be the same for both processes.
You started well by noting this.

At every point on each path there will be a well defined P and V.

You didn't answer the question about why you think w = 0 for the adiabatic irreversible path.

Path B and Path A could both reach a same state, P2, V2, and T1.

You are trying to specify P, V and T. You only specifiy two of these the third is not independent it is determined by the other two already specified
 
Hi Studiot,

Thanks for the discussion. To answer your quesion:

"why you think w = 0 for the adiabatic irreversible path"

my path B is a free expansion path. a free expansion path does zero work.
see Free_expansion in wikipedia.

And actually, I only try to specify two variables P and V, where T is kept constant as T1. sorry for not clear.
 
Wiki also says

.......which implies that one cannot define thermodynamic parameters as values of the gas as a whole. For example, the pressure changes locally from point to point, and the volume occupied by the gas (which is formed of particles) is not a well defined quantity.
 
Studiot said:
Wiki also says

yes, I am not picking any state variable in the middle of the free expansion. what i want to do is comparing the state function H enthalpy at the start and the end of the free expansion.

apparently, the enthalpy change for a free expansion is zero.

However, by taking another reversible Path A at constant T. the enthalpy change is not zero.

The thing is the start state (P1, V1, T1), end state (P2, V2, T1) of Path A and B are exactly the same. I want to expect the same enthalpy change for path A and B.

however, this is not the case. This confuses me a lot if we take enthalpy as a state function, who is independent of the paths.
 

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