Eng-Tips is the largest engineering community on the Internet

Intelligent Work Forums for Engineering Professionals

Register Log in

The jungle of Specific Heat Capacities and how to get it right

Status
Not open for further replies.
hirschaplin

hirschaplin

Petroleum
Jul 10, 2021
60
0
0
SE
The importance of a correct K/gamma-value for you inlet gas when selecting a compressor is of the utmost importance as you can read here
Hence the question how to navigate this jungle and get it right.

First of all, I understand the Cp and Cv is expressed at different pressures, temperatures and even various units of measurement.

A simple googling of "K value Specific Heat Capacities" or similar yield several tables with suggestions for various gases.

Here is a link to one of the results
The table provides Cp and Cv values both kJ/kg K and Btu/lbmoF and at approx. 20 deg C and 1 atm:
spec_heat_caps_epuf1x.png


The first confusion. Since the values are given at approx. 20 deg C and 1 atm, does this mean that if my actual gas composition is at a higher or lower pressure/temperature, the Cp and Cv values from this table will be incorrect for my particular case and discrepancies may occur?

Now the second confusion. Let us use Acetone from the table above as an example.

Cp/Cv in kJ/kg K yields: 1.47/1.32=1.11363636
Cp/Cv in Btu/lbmoF yields: 0.35/0.32=1.09375

Depending on which UoM I use, I will get different K values?!?! That can't be right?

My excel gas database does now consist of the following components:
Code: 
Methane
Ethane
Propane
n-Butane
n-Pentane
n-Hexane
n-Heptane
n-Octane
n-Nonane
n-Decane
n-Undecane
n-Dodecane
n-Tridecane
n-Tetradecane
n-Pentadecane
n-Hexadecane
n-Heptadecane
n-Octadecane
n-Nonadecane
n-Eicosane
2-Methylpropane
2-Methylbutane
2,3-Dimethylbutane
2-Methylpentane
2,3-Dimethylpentane
2,3,3-Trimethylpentane
2,2,4-Trimethylpentane
Ethylene
Propylene
1-Butene
cis-2-Butene
trans-2-Butene
1-Pentene
1-Hexene
1-Heptene
1-Octene
1-Nonene
1-Decene
2-Methylpropene
2-Methyl-1-butene
2-Methyl-2-butene
1,2-Butadiene
1,3-Butadiene
2-Methyl-1,3-butadiene
Acetylene
Methylacetylene
Dimethylacetylene
3-Methyl-1-butyne
1-Pentyne
2-Pentyne
1-Hexyne
2-Hexyne
3-Hexyne
1-Heptyne
1-Octyne
Vinylacetylene
Cyclopentane
Methylcyclopentane
Ethylcyclopentane
Cyclohexane
Methylcyclohexane
1,1-Dimethylcyclohexane
Ethylcyclohexane
Cyclopentene
1-Methylcyclopentene
Cyclohexene
Benzene
Toluene
o-Xylene
m-Xylene
p-Xylene
Ethylbenzene
Propylbenzene
1,2,4-Trimethylbenzene
Isopropylbenzene
1,3,5-Trimethylbenzene
p-Isopropyltoluene
Naphthalene
Biphenyl
Styrene
m-Terphenyl
Methanol
Ethanol
1-Propanol
1-Butanol
2-Butanol
2-Propanol
2-Methyl-2-propanol
1-Pentanol
2-Methyl-1-butanol
3-Methyl-1-butanol
1-Hexanol
1-Heptanol
Cyclohexanol
Ethylene
1,2-Propylene
Phenol
o-Cresol
m-Cresol
p-Cresol
Dimethyl
Methyl
Methyl
Methyl
Methyl
Methyl
Methyl
Diethyl
Ethyl
Ethyl
Methyl
Diphenyl
Formaldehyde
Acetaldehyde
1-Propanal
1-Butanal
1-Pentanal
1-Hexanal
1-Heptanal
1-Octanal
1-Nonanal
1-Decanal
Acetone
Methyl
2-Pentanone
Methyl
2-Hexanone
Methyl
3-Methyl-2-pentanone
3-Pentanone
Ethyl
Diisopropyl
Cyclohexanone
Methyl
Formic
Acetic
Propionic
n-Butyric
Isobutyric
Benzoic
Acetic
Methyl
Methyl
Methyl
Methyl
Ethyl
Ethyl
Ethyl
Ethyl
n-Propyl
n-Propyl
n-Butyl
Methyl
Ethyl
Vinyl
Methylamine
Dimethylamine
Trimethylamine
Ethylamine
Diethylamine
Triethylamine
n-Propylamine
di-n-Propylamine
Isopropylamine
Diisopropylamine
Aniline
N-Methylaniline
N,N-Dimethylaniline
Ethylene
Furan
Thiophene
Pyridine
Formamide
N,N-Dimethylformamide
Acetamide
N-Methylacetamide
Acetonitrile
Propionitrile
n-Butyronitrile
Benzonitrile
Methyl
Ethyl
n-Propyl
n-Butyl
Isobutyl
sec-Butyl
Dimethyl
Methyl
Diethyl
Fluoromethane
Chloromethane
Trichloromethane
Tetrachloromethane
Bromomethane
Fluoroethane
Chloroethane
Bromoethane
1-Chloropropane
2-Chloropropane
1,1-Dichloropropane
1,2-Dichloropropane
Vinyl
Fluorobenzene
Chlorobenzene
Bromobenzene
Air
Hydrogen
Helium-4
Neon
Argon
Fluorine
Chlorine
Bromine
Oxygen
Nitrogen
Ammonia
Hydrazine
Nitrous
Nitric
Cyanogen
Carbon
Carbon
Carbon
Hydrogen
Hydrogen
Hydrogen
Hydrogen
Hydrogen
Sulfur
Sulfur
Water

This list originates from table 2-164 in this PDF
The third confusion is that it seems nearly impossible to find simple table values for Cp/Cv for all components in this list, especially at approx. 20 deg C and 1 atm.

Or maybe not because the same PDF has table "2-196 Heat Capacities of Inorganic and Organic Liquids" which indeed seems to provide at least the Cp value for all items in the list but you need to be a Chemical Professor to understand how to extract the proper value at approx. 20 deg C and 1 atm since they only provide it at min and max temp...:
2-196_jxqfj3.png


Here again I think it is interesting to go back to the first confusion. As they provide a range, does it mean that the Cp value should be extracted by means of interpolation (?) at the actual gas operating temperature or shall I stick with approx. 20 deg C and 1 atm...?

Finally, as table 2-196 only provides the Cp value I understand that I can use the Cp value to get my Cv value by Cp-R=Cv but now I am confused again. Because by looking at this it seems like the R constant in this case is not 8.314... instead each entry in the list has it's own R.....(?):
Rconst_bakgii.png


If I can't obtain R then I guess I need to find Cv for each component in the list and get R by Cp-Cv=R...

Sorry but this is soooo confusing and tedious to solve. There must be a better way to find Cp and Cv for these components in a simple way that make sense.
 
Replies continue below

Recommended for you

Sort by date Sort by votes
Hi,
I recommend you buy a thermodynamic book or to go back to your university notes. That is the only way to get the things right.
Your ultimate resource should be Google or equivalent. Check for Mayer's relation.
Engineering is about hard work and there is no free lunch.
Good luck
Pierre
 
Upvote 0 Downvote
That is not very helpful.

Isn't the book I referenced exactly such a book you are referring to?

Mayer's relation require both Cp and Cv values and with that is all confusing with the basis of the values as I tried to explain above.

Every table you find with Cp, Cv and K values shows slightly different values depending on the source. Sometimes the values are given at different pressure and temperatures, hence my question for how to align it and get it right.

 
Upvote 0 Downvote
Hi,
1) R is a universal constant
2) Cp and Cv are molar calorific values, Cp-Cv =R
3) Cp is molar calorific value at P=cte
4) Cv is molar calorific value at v=cte
5) You don't calculate R, most of the time you calculate Cv =Cp-R
6) Tables are available on the web where Cp(T) is a polynomial function.

Korean data base to support your calculation:

Pierre
 
Upvote 0 Downvote
The first confusion: Yes. gas properties vary with temperature and pressure owing to the internal vibration modes and intermolecular interactions. The more complex the molecules the more complex the modes and interactions. Gases that are closer to ideal gases behave more as ideal gases behave. O2, N2, He, H2 should be similar. Complex hydrocarbons, not so much.

The second confusion: calculation has a problem from rounding error. The values are within 2% which is good for a 2 significant digit conversion.

The third confusion? That's not confusion, it's a lack of data.

The fourth Cp = Cv + R; R is a constant for ideal gases. Ammonia, for example, is far from an ideal gas.
 
Upvote 0 Downvote
Thank you guys, I think I have a solution to calculate Cp for all my substances as shown above and I have also learned how to calculate R which means I know have Cp, Cv and R.

One more question. To calculate Cp value I use TABLE 2-198 Heat Capacities of Inorganic and Organic Compounds in the Ideal Gas State from this PDF in the bottom of the table they provide two different equations to calculate Cp, equation 2 and equation 3. I don't see any explanation to when eqn. 2 or 3 should be used? Some of the tables entries are denominated with (equation 2) hence I guess equation 2 is applicable for them and equation 3 for all other table entries, is that correct?
table_2-198_c2qmmq.png
 
Upvote 0 Downvote
Latexman, I agree. See line 73 "Propylbenzene (eqn. 3)" and item 208 "Helium-4 (eqn 2)"

The unnumbered equation appears to cover all the rest.
 
Upvote 0 Downvote
Ok I am trying to establish the Cp for Methane now with that formula.

C1 * 1E-05 = 0,333*0,00001 = 0,00000333
C2 * 1E-05 = 0,7993*0,00001 = 0,000007993
C3 * 1E-03 = 2,0869*0,001 = 0,0020869
C4 * 1E-05 = 0,416*0,00001 = 0,00000416
C5 = 992

J/(kmol K) * 2,390059E-04 = J/(kmol K) * 0,0002390059 = Btu/(lbmol·°F)

T (deg C) = 20
T (deg K) = 293,15

Cp = (C1+C2*(C3/293,15/SINH(C3/293,15))^2+C4*(C5/293,15/COSH(C5/293,15))^2)*2,390059E-04 = (0,00000333+0,000007993*(0,0020869/293,15/SINH(0,0020869/293,15))^2+0,00000416*(992/293,15/COSH(992/293,15))^2)*0,0002390059 = 2,75853E-09 = 0.00000000275853

Which obviously is incorrect. I would expect that Cp should be approx. 0.558 Btu/(lbmol·°F at 20 deg C.

Any ideas what is wrong?

 
Upvote 0 Downvote
I think this thread has THE most accurate title ever seen. It really is a jungle.

Every time I think I have a breakthrough, I am again and again and again put back in my place...

I found this interesting website
I followed their formula Cp = A + B*T + C*T^2 + D*T^3 + E*T^4 where Cp in kJ/kg-mol, T in K which resulted in that I get Cp for Methane at 20 deg C=35,9699614184067 kJ/kg-mol but for some reason it seems impossible to convert a value in kJ/kg-mol to kJ/kg K or Btu/lbm·R or Btu/lbmoF. Hence I can't even verify if the result is somewhat reasonable...

This shitty topic makes me feel like an infant... for example try to convert with any of these converters:

Gahhhhhhh [ponder]
 
Upvote 0 Downvote
Some days are like that.

From A kilogram-mole (kg-mol) is a derived metric SI (System International) unit of amount of substance. The kilogram-mole is that amount of substance that contains the same number of elementary entities as there are atoms in 12 kilograms of carbon 12.

It appears you need to divide by the molecular weight of Carbon (12) and multiply by the molecular weight of the substance to get the mass.
 
Upvote 0 Downvote
Hi,
1 kg-mole =1000 moles >>>> for CH4 MW =16kg/kg-mol or 16 g/mol.
The quantity expressed in KJ/Kg-mol K should be divided by the molecular weight to get the right conversion in Kj/Kg K., not as written above.


If you need a professional unit convertor, visit Katmar software. Katmar is a member of this forum or Google Uconeer unit converter.

Pierre
 
Upvote 0 Downvote
Upvote 0 Downvote
@pierreick you are my saver like always. 35,9699614184067/16,0426=2,24 kJ/kg K which match very well with the value in my reference table that is 2,22 kJ/kg K.

@MintJulep that seems like a sweet program which I maybe can use for verification purposes.

@shvet I already have a working method that give me the numbers I need using multiple softwares. For example HYSYS, ChemCAD and various vendor proprietary selection and calculation tools... What I am trying to do now is to replace these various softwares with 1 single excel sheet to basically reduce the time I need to spend to get to the answers I need. I am treating the results in my excel sheet as a rough sketch of reality that I am using for initial sizing and performance determination. Once the project become real, the results from my excel has to be verified by us and by vendors when applicable.

I don't appreciate the term "basic". The reason why it is not basic is because there is no single source that provide the full perspective. In 3 of my vendor softwares, there is a gas mixing functionality. All 3 of them provides Cp and K values as properties. None of them are declaring UoM for these properties:
methyl_dpql5w.png


And they are definitively not telling at which temperature/pressure the values are obtained at. And if you change the temperature in their programs, the Cp and K value doesn't change as it seems.

The lack of clear and unquestionable information makes it very annoyingly difficult. I am not able to create the level of clarity that I need.

@pierreick or anyone else, did you look at the above equation with c1, c2, c3, c4 and c5? I am starting to think that perhaps the formula was correct but that the constants was the problem:
C1 * 1E-05 = 0,333*0,00001 = 0,00000333
C2 * 1E-05 = 0,7993*0,00001 = 0,000007993
C3 * 1E-03 = 2,0869*0,001 = 0,0020869
C4 * 1E-05 = 0,416*0,00001 = 0,00000416
C5 = 991,96

It I change it to:
C1 * 1E+05 = 0,333*100000 = 33300
C2 * 1E+05 = 0,7993*100000 = 79930
C3 * 1E+03 = 2,0869*1000 = 2086,9
C4 * 1E+05 = 0,416**100000 = 41600
C5 = 991,96

It results in: 35497,55 J/(kmol·K) = 35497,55/1000=35,49755 kJ/(kmol·K) = 35,49755/16,0426 = 2,21 kJ/kg K which is very good and close to my reference table value of 2,22 kJ/kg K. Hence I think the equation work as intended now.

But can anyone explain why they write 1E-05 and 1E-03 in the table header when 1E+05 and 1E+03 is correct....? No remark or clarification about this in the table, right?
23232_hsjpcw.png
 
Upvote 0 Downvote
Upvote 0 Downvote
@IRstuff, thanks!

Ok guys, tonight there is a smile on my face.

Finally the Cp, Cv and K calculations work as intended:
Sk%C3%A4rmbild_2023-08-10_001816_oioq9x.png


Now I just need to adjust the few lines which requires eqn. 2 and 3. Then I should have fairly good values for Cp, Cv and K for all 231 substances in my database. Which now are based on the actual operating temperature of the gas stream.

Thank you all for your help.

EDIT:
Sorry, the image becomes rather small after upload.
 
Upvote 0 Downvote
Hi, right now you got data at 1 bar, 20 C for ideal gas.
Is that the requirement? If not, you need to calculate the C =C ideal gas + C residual, both for C at p=cte and C at v=cte.
P*v=Z*R*T for real gas.
For these calculations, Z and C residual you need to use an Equation of state. Let say Peng Robinson, Soave Redlich and Kwong or others.
Again a good thermo book and Calculus notes will help you
Good luck.
Pierre
 
Upvote 0 Downvote
Status
Not open for further replies.

Similar threads

Ameen1985
  • Locked
  • Question
Should the air specific heat ratio be included in the ideal gas law ? 1
Replies
2
Views
6
Snickster
Snickster
edwardmp2009
  • Locked
  • Question
Interpretation of Heat exchanger nameplates
Replies
3
Views
17
georgeverghese
georgeverghese
MechEng92
  • Question
How should I work out Wattage for a heat exchanger pad heater?
Replies
9
Views
28
pierreick
pierreick
Papps
  • Locked
  • Question
Operation Of Heat Exchanger Above The Overall Heat Transfer Coefficient 1
Replies
3
Views
8
Desmond_Aubery
Desmond_Aubery
_kon
  • Locked
  • Question
Determining the flow on the counter-flow heat exchanger
Replies
5
Views
19
EdStainless
EdStainless
Back
Top