Specific Heat Capacity to Calculate K

[dummiboi]

Hi,

I'm trying to calculate K using Cp and the equation K=Cp /(Cp-R).

I looked up Cp in the JANAF tables and in a CRC book and the Cp values were listed at 100 KPa. I'm trying to find K at STP does it matter that Cp is taken at 100 and not 101 KPa? How do I convert it or find it at standard atmospheric pressure?

Also, I'm looking to find Cp values for these gases for a range of 50 - 300 F (283-422K). Can anyone recommend any books where I can look these values up? They aren't in my CRC book or in the JANAF tables that I looked at, and my CRC book only goes down to 298 K.

Hexane
Propylene
iso-Butane
n-Butane
iso-Butylene
Butylene
Trans 2 Butene
CIS 2 Butene
iso-Pentane
n-Pentane
Carbon Tetrachloride

Any help would be appreciated.

Thanks much,
Jesse

 

[MortenA]

For pure component data (and free) noting beats

http://webbook.nist.gov/chemistry/

Best regards

Morten

 

[sailoday28]

The equation K=Cp /(Cp-R). is valid only for a perfect gas.
Try what MortenA suggests or go use an equation of state combined with the low pressure specific heats to get K.

Regards

 

[25362]

Cp-Cv = T([∂]P/[∂]T)_V([∂]V/[∂]T)_P, which for an ideal gas results in Cp-Cv = (TR/V)(R/P) = R.

Applying the Berthelot equation to express the partial differential quotients, neglecting the terms which appear only at very high pressures, one gets

Cp-Cv = R (1+1.69 Pr/Tr³)​

or when using the van der Waals equation,

Cp-Cv = R + 2aP/RT²​

or alternatively, if you have Cp and the reduced properties Pr and Tr, one article in ChE (March 14,1977) gave for real gases:

Cp-Cv = R [1 + (Pr/Tr²)[0.132+0.712/Tr)²]​

then, k = Cp/Cv = Cp/[Cp-(Cp-Cv)]

 

[dcasto]

Chapter 13 of the GPSA data book has some tables with Cp for the componets at various temperatures. It has methods for determaing Cp of mixtures and graphs based on Mole Wt.

 

[dummiboi]

Thanks all for your help.

What I'm trying to do is to find K for different mixtures of the gases listed above without knowing the pressure of the gas. I initially wanted to go with K=Cp/Cv, but I could not find Cv, so I tried to use k=Cp/Cp-R. I know this equation is only for ideal gases, but will it not work at all or will it just have an error associated with it?

What is the GPSA book that was referred by dcasto?

Thanks again,
Jesse

 

[dcasto]

Some bookstores that specialize in engineering books have it or you can go to

http://www.gasprocessors.com

 

[sailoday28]

25362 (Chemical)
Using
Cp-Cv = T(?P/?T)V(?V/?T)P,

when using the van der Waals equation

Can you provide a reference or indicate major assumptions for


Cp-Cv = R + 2aP/RT^2

Regards

 

[25362]

To sailoday28,

The van der Waals equation is not the most preferred EOS. Anyway, here are the assumptions, as far as I can remember:

The basic equation: (P+an²/V²)(V-nb) = RT

for one mol (n=1): (P+a/V²)(V-b) = RT

([∂]P/[∂]T)_V = R/(V-b)

([∂]V/[∂]T)_P ~ V/T - b/T +2a/RT² - 3abP/R²T³

neglecting 3abP/R²T³

T([∂]P/[∂]T)_V([∂]V/[∂]T)_P [≈] R + 2a(P+a/V²)/RT² = R + 2aP/RT² + 2a²/RV²T²

Again, neglecting the last term

Cp-Cv = T([∂]P/[∂]T)_V([∂]V/[∂]T)_P [≈] R + 2aP/RT²

The CRC manual (77th ed.) gives the values for a (a measure of intermolecular attractions) and for b (a measure of the volume taken up by the molecules themselves) for most of the gases listed by dummiboi, which when knowing the actual system conditions would enable one to see when the above assumptions are acceptable or have just a qualitative value.

 

[sailoday28]

(Chemical25362
I agree that VDW is not the most preferred.

I didn't know your assumptions, but since a and b generally would be small compared to specific volume your derivation makes sense.
However,even for low pressures, the approximation may be inaccurate for low temperatures.

Regards