R410A specific heat capacity cp

[Luca Menegozzo]

Hi all,

I'm calling CoolProp.dll version 6.4.3 from Matlab to calculate R410A properties.
To get the specific heat capacity at constant pressure (cp) of the saturated vapor at T = 277.65 K I would do:

cp = calllib('coolprop', 'PropsSI', 'C', 'T', 277.65, 'Q', 1, 'R410A') = 1.1726e+03  J/kgK

Which is wrong (saturation tables say 780.41 J/kgK).
Googling around I found this instruction for pseudo-pure fluids, and then this answer here in the group, so I replaced the vapor quality specification with a nearly zero density, and I get a reasonable value:

cp = calllib('coolprop', 'PropsSI', 'C', 'T', 277.65, 'D', 1e-10, 'R410A') = 774.7494 J/kgK

That said, I have two questions:

1) Is PropsSI('C', 'T', T, 'D', 1e-10) a sort of cp_ideal_gas(T)?
2) How can I get cp of saturated and subcooled liquid? 

Thank you so much
Luca

[Ian Bell]

Where do you see tabulated values for heat capacity of saturated vapor in the linked PDF? Sometimes you have c_sat presented instead of c_p, where c_sat is defined as c_sat = T*dsliq/dT

I run a variant of your example in Python:

import CoolProp.CoolProp as CP, numpy as np

Dsat = CP.PropsSI('Dmass','T',277.65,'Q',1,'R410A')

for Dmass in np.linspace(Dsat, 1e-10, 30):

    print(Dmass, CP.PropsSI('Cpmass','T',277.65,'Dmass',Dmass,'R410A'))

and I get:

35.29803873217535 1172.5569947960796
34.08086498279344 1151.3525597730506
32.86369123341153 1130.9814999795706
31.646517484029623 1111.393575884487
30.429343734647716 1092.542285393608
29.212169985265806 1074.384542922836
27.994996235883896 1056.8803933295706
26.77782248650199 1039.9927563665792
25.560648737120083 1023.687197926035
24.343474987738173 1007.9317248522664
23.126301238356263 992.6966005355085
21.909127488974356 977.954178868317
20.691953739592446 963.6787544617603
19.474779990210536 949.8464272886421
18.25760624082863 936.4349801529481
17.040432491446722 923.4237675843956
15.823258742064812 910.7936149292543
14.606084992682902 898.5267265576772
13.388911243300996 886.6066022369793
12.171737493919085 875.0179608326306
10.954563744537179 863.7466705964861
9.737389995155269 852.7796853871298
8.520216245773362 842.1049862418107
7.303042496391452 831.7115277848243
6.085868747009542 821.5891890145701
4.868694997627635 811.7287280619623
3.651521248245725 802.1217405573228
2.434347498863815 792.7606212820981
1.2171737494819084 783.6385288164031
1e-10 774.7493529240827

I get the same results in REFPROP. I think your values used for comparison are the problem.

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[Luca Menegozzo]

Yes, that's right, I was looking to the results given by the ideal gas cp polynomial.

Thank you!