Do a state function be multu-valued function

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Discussion Overview

The discussion revolves around whether a thermodynamic state function can be a multi-valued function, specifically in the context of enthalpy and steam tables for pure water. Participants explore implications for thermodynamic laws and the nature of state variables.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that a state function should be a single-valued function of independent variables, citing the example of enthalpy having the same value at different pressures and temperatures for pure water.
  • Others argue that the existence of multiple values for enthalpy indicates that thermodynamics may not be an exact science, suggesting that the data or definitions may be incorrect.
  • One participant emphasizes that state variables must be single-valued to maintain the integrity of the Gibbs-Duhem relation and to avoid path-dependence in state diagrams.
  • Another participant mentions that the steam tables published by recognized institutions, which show multiple values for state functions, challenge the conventional understanding of state functions.
  • Some participants propose that the existence of multiple values in steam tables does not necessarily imply a problem, as they reference a response from the journal editor stating that state functions can have multiple values.
  • One participant shares their experience of writing an article addressing the issue with steam tables and proposes a method for measuring water properties correctly.

Areas of Agreement / Disagreement

Participants express disagreement regarding the nature of state functions, with some insisting they must be single-valued while others contend that multiple values can exist without contradiction. The discussion remains unresolved, with competing views on the implications of the steam tables and the definitions of state functions.

Contextual Notes

Participants reference the Gibbs phase rule and the principles of equilibrium thermodynamics, indicating that definitions and interpretations may vary. There are also mentions of specific publications and standards, suggesting a reliance on established literature while questioning its accuracy.

Who May Find This Useful

This discussion may be of interest to students and professionals in thermodynamics, researchers examining the properties of water, and those involved in the development of scientific standards and measurements.

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Does a state function be multi-valued function

A thermodynamic state function should be single valued function of independent varibles.
In case of steamtables of pure water, there is same entahlpy (U=2000 kJ/kg) at temperature T1=700K and pressure P1=63.458 MPa, and at T2=700K and P2=456.356 MPa. Thus U is a multiple valued function for pure water. How it can be explained with the basic laws of thermodynamics.
 
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The temperature is the same...?Anyway,it doesn't really matter.Enthalpy is denoted traditionally in thermodynamics by H,BTW...

So what is the problem...?

Daniel.

P.S.It's a REAL gas...:wink:
 
Yes, enthalpy is generally represented by H. Let us read H for U.

Thermodynamics laws are applicable to all systems, real or ideal.

If we consider T and H as independent variables, it is impossible to predict the right value of P. The meaning of two values of P is that P is not an exact solution. This way- thermodynamics is not an Exact Science. Everyone knows that thermodynamic is an exact science, therefore the two values of P in the above situation are incorrect.

Let us further exemplify the above situation. We have a container filled with water at T=700 K and P=63.485 MPa. Since there is same H (2000 kJ/kg) for P= 63.458 MPa and 456.356 MPa at T= 700 K, it means we can pressurize (from 63.458 to 465.356 MPa) the container without any work. In other words, we can increase the pressure in a system of constant V and T without doing any work. If it is possible, we can develop a Carnot cycle to solve the world energy problem with no expense.

If a state function has multiple values, either the definition is incorrect or the data.

Thus the values of enthalpy are incorrect in steamtables.
 
Who said the volume is kept constant...?:bugeye:

Daniel.
 
Let us keep is simple. A state function can have multivalues or not.
 
Certainly.
 
Yes,u may want to check again the exact wordings of the principles in CTPCN formulation of the equilibrium thermodynamics.

Daniel.
 
Any two state variables should define completely the pure system of constant mass. You can read any book on thermodynamics.
 
Adjust add "in a phase of a pure system of constant".

"Nothing is more practical than a good theory"
Does it say something to you!
 
  • #10
So what,what does my signature have to do with anything...?

Daniel.
 
  • #11
Dear Daniel:

If someone signs the quotation, he knows about the theory and don't write any comments without thinking.

The Gibbs phase rule is given in all the books, there is no need to cite any particular book.

Best wishes

Mahendra
 
  • #12
State variables have to be single valued. The Gibbs-Duhem relation relies on this. If they weren't single valued, then a closed path on a state diagram could result in a change of the state variable.. that is the value of the variable would be path-dependent, which is the definition of something that is not a state variable, but a process variable.
 
  • #13
Yes, you are right. A state function has to be single valued function. It is a definition or based on the some relation. It is not the question, the question is that the steam Tables for pure water which is published in a NIST and AIP journal, J. Phys. Chem. Ref. Data, 2000, has multiple values for U, H and G.

It is really amazing the institutes producing standards for whole scientific community, do not know (or do not accept) that a state function should be single valued function.
 
  • #14
Instead of wondering how & why this was possible,why don't u write a mail to them and tell them they're deadly wrong...:wink:

Daniel.
 
  • #15
I wrote an article on it to demonstrate the problem with the steam tables. Similarly, I proposed a method to measure the properties of water (liquid) correctly. I have big discussion the editor of JPCRD and the authority.

Their reply is that a state function can have multiple values. So, the steam tables of water has no problem.

If anyone is interested in reading it. I can send a copy. Just send me your email. my email is mahendra@iie.org.mx

If the thermodynamic properties of water are incorrect, there is problem in understading the natural processes on the earth.
 

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