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# Cp/Cv for gas or for both gas and liquid!!4

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## Cp/Cv for gas or for both gas and liquid!!

(OP)
Hello,

As far as I know, Cp/Cv is a parameter for gas. But during the simulation in ASPEN HYSYS if I pick up a liquid stream and enter necessary parameters like P, T and mole or mass fraction then it shows the corresponding parameters of liquid and I also get the value of Cp/Cv.

I am not really getting the point about this parameter in case of liquid.

I need help regarding this.

Many Thanks

### RE: Cp/Cv for gas or for both gas and liquid!!

It is a ratio of two numbers that are defined for liquids. I don't know that the ratio has the same meaning in a liquid as in a gas, but it can be calculated.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)

zdas04,

If it is applicable in liquid then how could I calculate that?
In the case of gas I had used Cp/Cv=Cp/(Cv-R)
But in liquid, how?

Thanks!

### RE: Cp/Cv for gas or for both gas and liquid!!

Since a liquid is very nearly incompressible, would suspect Cp would be almost identical to Cv.

### RE: Cp/Cv for gas or for both gas and liquid!!

For an incompressible liquid, Cp/Cv=1.0.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Cp/Cv for gas or for both gas and liquid!!

Like the others, I think calculating Cp/Cv of a liquid is a useless activity. AspenTech can best answer this question. Their website has a CONTACT US.

Please let us know the outcome.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Cp/Cv for gas or for both gas and liquid!!

shiplu48,
if the question is how your software calculates cp and cp/cv then ask technical support,
if the question is general (how software applications calculate cp and cv for both gas and liquid state) you may find answers in many textbooks (see properties of gases and liquids, to mention one),
for example for CV you may utilize a EOS to calculate H and V (plus derivatives),
different software applications export these properties plus derivatives (see for example Nist Refprop or Prode Properties) other applications may calculate derivatives numerically but finally you get your value,
take care that for liquid phase std. EOS (such as Peng-Robinson and Soave-Redlick-Kwong) may show large errors for values of cp, cv, speed of sound, isothermal compressibility etc.
when available you should select methods with specific parameters for each fluid (to calculate H, V etc.)
there are posts (at eng-tips and cheresources) comparing accuracy of std. and modified versions of Peng_Robinson and Soave when calculating liquid properties,
if an accurate model is available (see for example Steam Tables) that should be the preferred option.

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)
apetri,
Thank you for your explanation. That things help a lot.
As I have searched the Steam Tables, there are just properties at different T and P.
There is no mention of procedure of cal calculation. Would you please give me the link for calculation or
link of posts (at eng-tips and cheresources) comparing accuracy of std. and modified versions of Peng_Robinson and
Soave when calculating liquid properties?

I would also like to thank georgeverghese,zdas04, Latexman for sharing their knowledge.

Many Thanks.

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)

I have already visited the site and have found several values for water in liquid phase.
Which equations were used to find that values, if I want to find Cp or Cv?
Could you please mention the name of equations that have been used in case of liquids?

Many thanks.

### RE: Cp/Cv for gas or for both gas and liquid!!

I see that apetri's post and others' have been quite explanatory. If you include molten metals and condensed 'permanent' gases as liquids, the picture becomes even more complex. I don't know of any encompassimg equation. The following link may clarify some points:

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)
Thanks, 25362 for the link.

### RE: Cp/Cv for gas or for both gas and liquid!!

to apetri

Could you please share some links to eng-tips and/or cheresourses discussions about EoS accuracy?

### RE: Cp/Cv for gas or for both gas and liquid!!

Stoner Pipeline Simulator (now DNV-GL Synergi Pipeline Simulator) always used Cv/Cp for liquids, rather than the more typical ratio for gas, Cp/Cv, which was always a point of much confusion. Not sure if they have ever changed it.

### RE: Cp/Cv for gas or for both gas and liquid!!

In theory, from thermodynamics, we have, for any fluid
dH = dU + d(PV)
At const. pressure
Cp.dT = Cv.dT + P.dV

Dividing through by Cv.dT
Cp/Cv = 1 + P.dV/Cv.dT

Here, dV is the incremental change in real fluid molar volume of the liquid at constant pressure over the temp interval dT. In SI units, P= N/m2, Cv = kJ/kgmole/degK, dV = m3/kgmole. Interpolating with this NIST data for example, I get Cp/Cv to be 1.018 at 330degK using this expression (with approx. data from 325degK to 335degK), 1atm while that from NIST would be 1.048. This value from NIST also matches up with data in Perry at 50degC, 1atm(table 2-355 in the 7th edition).

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)
Dear georgeverghese,

It was a good one.
What was the range of fluid molar volume change, initial volume and final volume?
Why don't you come up with a full math. It would be clear enough.

### RE: Cp/Cv for gas or for both gas and liquid!!

see The Properties of gases and Liquids , chapter 6, Heat Capacities of Real gases (previously suggested),

cp = (dH/dT)p
cv = (dU/dT)v

there are different ways to calculate these values, a table of values, a EOS etc.
with a EOS you can calculate cp=(dH/dT)p , V , dV/dP , dV/dT
and finally cv

### RE: Cp/Cv for gas or for both gas and liquid!!

(OP)
Then it is valid to have Cp/Cv for liquid!

### RE: Cp/Cv for gas or for both gas and liquid!!

you can calculate cp, cv, speed of sound, compressibility etc. for liquids (as for gases),
however take care that results in some cases may show large errors (see previous posts)

### RE: Cp/Cv for gas or for both gas and liquid!!

Yes, Cp/Cv for a liquid is valid, but it's not very useful and prone to large errors.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Cp/Cv for gas or for both gas and liquid!!

Error in my last response

a) The units for pressure should be in kN/m2, not N/m2 to keep things consistent in SI units. With this, the value obtained for Cp/Cv is 1.00033 and does not match up with Cp/Cv calculated from the NIST tabulation.
b) The error is due to the expression for dU, which is not just Cv.dT; see the full expression 4-45 in Perry Chem Engg Handbook 7th edition, for which I'm having trouble computing one of these terms.

### RE: Cp/Cv for gas or for both gas and liquid!!

The expression 4-45 in Perry is

Cp - Cv = T.(∂V/∂T)P.(∂P/∂T)V

With additional information on the density variation of subcooled liquid water with pressure and with temp(page 2-311, table 2-355), it is possible to confirm the value for Cv for a given Cp value, from which Cp/Cv can be computed. I have just verified this. For example, in the temp interval 40-50degC, pressure interval 50-200bar, Cp/Cv computed is 1.060, while tabulated value is 1.043.

### RE: Cp/Cv for gas or for both gas and liquid!!

To georgeverghese, in that range of pressures and temperatures, the NIST webbook provides a series of values.

### RE: Cp/Cv for gas or for both gas and liquid!!

@25362, Previous response provides the theory and manual calc route for real fluid Cp/Cv for water or any other liquid or vapor stream for that matter.

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