Thermodynamic properties calculation

[nalasimbha]

Hi,

I would like to know what equations are used to calculate thermodynamic properties like enthalpy, Cp, entropy at a given temperature and pressure. I know i can use standard tables for these values, but I am curious as to how these are calculated. I am looking for equations in which i can substitute values and get the properties.

Thanks

 

[dcasto]

Every thermobook on my shelf has them. The CRC has some too with the constants in tabular form.

 

[sailoday28]

Two ways are:
1-Given an equation of state and specific heat at (very) low pressure, the properties may be calculated requiring integration.
2-Given specific heat at low pressure and Availability,
A=U-TS, the properties may be calculated requiring differentiation.

 

[zdas04]

If what you are looking for is the answers instead of the questions I use REFPROP.exe from NIST. You define your fluid and then it gives you the parameters you are looking for at the pressure/temperature you input. It is the most powerful tool I've found for a practical engineer who needs to use this sort of information instead of needing to derive it.

David

 

[nalasimbha]

@zdas04 - I do use refprop to get the properties. But I was curious as to how the properties were being calculated. The property calculations in refprop are based on complex algorithms. I was wondering if someone could direct me as to what equations are being used.

 

[Twoballcane]

Ummm...have you ever taken a thermal class before? Not to be funny. Even though you have the equations, do you know how to use them practically?

Tobalcane
"If you avoid failure, you also avoid success."

 

[nalasimbha]

@ Twoballcane: Not to be rude..what are u getting at? All I am trying to figure out is how are the properties say in a saturated steam table obtained for a given Tsat or Psat?

 

[FOURe]

Values are based upon experimental measurements for a given temperature range and having some kind of least square curve fit done when it comes to the experimental data values for given thermodynamic relationships.

Here is a good example when it comes to enthalpy vs temperature values when the ideal gas assumption is used, enthalpy is a function of temperature only -- also, please note that at the reference conditions having temperature of 298 [K] and pressure of 1 [atm], enthalpy for basic elements such a s carbon, hydrogen, sulfur, oxygen and nitrogen is equal to zero!

​

http://www.engineering-4e.com

 

[MortenA]

nalasimbha your questions are very fundamental and thus hard to answer here. However - specifically for steam he values are based on lab data. So are all other pure component data and interaction parametres.

Best regards

Morten

 

[nalasimbha]

@Foure and MortenA: Thanks!

 

[sailoday28]

FOURe
The reason enthalpy of a perfect gas is a function of temp (only) is that CP at low pressure is a function of temp.

dh=CpdT+ d(p*tau)/dtau|v dv = Tds - pdv

where Cp is spec heat, p is pressure , tau = 1/T where T is absolute temp v is spec vol, s entropy

For a perfect gas pv=RT p*tau= R/v Therefore
d(p*tau)/dtau|v= 0 and dh=CpdT
Since Cp at low pressure (perfect gas) is a function of T, then h= hreference + integral CpdT ( from Treference to T).

 

[sailoday28]

correction

equation from 1st and 2nd laws should be:
de=CvdT-d(p*tau)/dtau|v dv = Tds - pdv
which shows that internal energy is a function of temp only for a perfect gas.
Similarly
dh=cpdT+ d(v*tau)/dtau|p dp = Tds +vdp

For pgas d(v*tau)/dtau|p=0 and therfore h is function of T,

 

[Twoballcane]

nalasimbha, my apologies if I came across wrong, I was trying to gage your needs. If you have taken a class, then the equitation should be in your text book. And if you don't know how to use them, than we can site the first and second law of thermodynamics.

Tobalcane
"If you avoid failure, you also avoid success."

 

[vpl]

nalasimbha

I'll be a bit more blunt than the previous posters: Are you requesting this information for a school project or homework?

Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[nalasimbha]

I think I should have put the question in better words. I am not looking for the laws of thermodynamics. What i was exactly interested was how the numbers in a thermodynamic property tables (for fluids such as steam, nitrogen, R134a etc) are calculated. Are they interpolated values based on experiments at specific points of temperature and pressure or can the properties be evaluated from theoretical equations by just knowing temperature and pressure (without knowing Cp, k, rho, etc).

If they are based on experimental data like MortenA said, it answers my question. If not can some one just show to evaluate h,s,Cp,u,rho etc say for saturated steam at 10bar?

And this is not for any homework or project.

 

[davefitz]

As an example of how NIST developes a correlation for thermophysical properties, see the below link for the canaonical form of the equation of state for H2O, and how succeeding derivatives yields each thermodynmaic propperty:

<

http://www.nist.gov/srd/PDFfiles/jpcrd242.pdf>

 

[sailoday28]

Davefritz: As a side note, refer to my first comments
A=U-Ts, etc and equation 5.20 of your reference to NIST.

 

[PaoloPemi]

I work mainly in Excel and I use Properties for calculating all the properties which I need in Excel cells, at

http://www.prode.com

you can download a free (limited) copy, the program works with a database which includes temperature dependent correlations for a large number of fluids plus several equations of state for calculating departure from reference (0) pressure to operating conditions, I would recommend reading "the properties of gases and liquids" , Reid, Prausnitz, Poling, for all the details including the equations.

 

[hacksaw]

the properties requested in the original post are derived from the equations of state correlations and supplemented by the enthalpy data, etc. The data are obtained by extensive lab testing and reduced to correlations. Thermodynamic relationships are then used to generate the properties being sought.

Less accurate estimates may be obtained from the equations of state such as Redlich-Kwong, etc. that are less precise though less complicated, but you still need the enthalpy data.

Numerically you have to generate code to construct partial derivatives of the basic data.

All of the references sited by other posters are a good starting point.

Good luck, the effort is quite the learning experience