# Do a state function be multu-valued function

1. Feb 23, 2005

### mpv55

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.

Last edited: Feb 23, 2005
2. Feb 23, 2005

### dextercioby

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...

3. Feb 23, 2005

### mpv55

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.

4. Feb 23, 2005

### dextercioby

Who said the volume is kept constant...?

Daniel.

5. Feb 23, 2005

### mpv55

Let us keep is simple. A state function can have multivalues or not.

6. Feb 23, 2005

### Bystander

Certainly.

7. Feb 24, 2005

### dextercioby

Yes,u may want to check again the exact wordings of the principles in CTPCN formulation of the equilibrium thermodynamics.

Daniel.

8. Feb 24, 2005

### mpv55

Any two state variables should define completly the pure system of constant mass. You can read any book on thermodynamics.

9. Feb 24, 2005

### mpv55

"Nothing is more practical than a good theory"
Does it say something to you!

10. Feb 24, 2005

### dextercioby

So what,what does my signature have to do with anything...?

Daniel.

11. Feb 24, 2005

### mpv55

Dear Daniel:

If someone signs the quotation, he knows about the theory and donot 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. Feb 24, 2005

### kanato

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. Feb 25, 2005

### mpv55

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. Feb 25, 2005

### dextercioby

Instead of wondering how & why this was possible,why don't u write a mail to them and tell them they're deadly wrong...

Daniel.

15. Feb 25, 2005

### mpv55

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.