Heat Capacity Question

[jproj]

The specific heat capacity (or an equation for it) for water is well documented for both liquid and ideal gas states. What about the transition phase? Is there any way to calculate Cp & Cv for two phase water (steam & liquid)? Any advice or references are greatly appreciated.

jproj

 

[DeltaCascade]

What do you mean by transition phase? I only know of solid phase(there can be many solids phases), liquid phase and vapour phase. Supercritcal water could be described as a special case of the vapour phase (or liquid phase, depending upon how you look at it)....

Maybe you just need to check steam tables, enthalpy-presure-temperature diagrams, and 1st year engineering/chemistry fundamentals?? ... you have enthalpy of phase change to account for, which is not Cp but delta-Hvap... Delta-Hvap calculation is also well documented.

Let us know if we can help more, or if I am just missing something.

Good luck.

 

[Samiran]

If you mean 2-phase i.e partially steam & partially water, why not use the mixing rule to get the overall Cp.

 

[jproj]

By transition phase, I mean the region between steam and liquid. I am trying to calculate the mass flow rate for a choked two-phase flow from a boiler blowdown. For this calculation, I need k (ratio of Cp/Cv). I have looked in my fluids book, my thermo book, and perry's. All say "the relationship between Cp and Cv for mixed phase (steam & liquid) is "complex and not delt with in this book". Thus I am stuck trying to figure out the relationship between the two, and also for finding the value for Cp in the tranmsition. Cp for liquid and ideal gas states are easily found. Any insight is much appreciated.

jproj

 

[MortenA]

There are no "region between liquid and steam (vapour)" but of course there is systems where water and steam exists together.

Best Regards

Morten

 

[boilerguy]

If you just want the flow rate, can you take another approach and solve the blowdown flow rate from a material balance around the boiler?

i. e. Blowdown Flow = Feedwater Flow - Steam Rate

This type of calculation will get you in the ballpark and will be pretty accurate for hourly or daily averages, provided your boiler is close to steady-state operation.

 

[jproj]

MortenA: there is most definately a region between saturated liquid and saturated vapor where (as you stated) water and steam exist together. (It's called the two phase region...look at a P-V or T-S diagram). Temperature and pressure are constant, but all other properties vary with composition.

boilerguy: This unit is still in the design stage and there's no data available. The blowdown flow rate is going to depend on the choked flow rate from the boiler to an atmospheric blowdown tank for the current pipe size (that's all I have to work with).

Currently, all I have is one equation that uses the ratio of Cp/Cv to calculate the choked flowrate.

Thank you for the responses, any additional advice is appreciated.

jproj

 

[DeltaCascade]

MortenA is correct. Sorry, there is no third phase. What you have is two phases in thermodynamic equilibrium. You may want to review those fundamentals.

The two phase flow question, on the other hand, is totally different, and quite complex. It is a posting which i would much like to follow. jproj, you may want to repost it if interest dies here .. it is not a heat capacity question, at all.

Wished i had time to review my references .. but blowdown valve manufacturers should be able to help you. If you had blowdown heat recovery exchanger, you MAY not have flashing to two phase to worry about....

 

[boilerguy]

In the boilers I work with, the blowdown flow measurment element is upstream of the blowdown control valve. This arrangement ensures that the flow meter only sees one-phase (liquid) flow.

"The blowdown flow rate is going to depend on the choked flow rate from the boiler to an atmospheric blowdown tank for the current pipe size (that's all I have to work with)."

This sounds like you are not planning on having a blowdown control valve and are relying on a small line size to restrict and control blowdown flow; is this correct? If so, I would strongly recommend using a somewhat larger line size and add an orifice plate that can be changed to adjust blowdown flow. The orifice plate should probably be as close to the blowdown tank as possible. Two phase water/steam flow in piping can give all kinds of headaches with pitting, corrosion, and erosion.

 

[MortenA]

I was thinking about a "third phase" when i postulated that "there is no region..". But apperantly i misuderstood you. Remember that water "boils instantly" Its not like a mix of HC's where you get 2 phases with different composition. All the water in a pot of course does not evaporate instantly - but thats because of the heat of evaporation and the duty of the stove. If you maintained a temperature +100 eventaually all the water would evaporate - in contrast to a mix of HC's where at some P, if you raise the temperature above the boiling point eventually a new equlibrium would be reached where a liquid phase (at its boiling point) with one composition would be in ballance with a gas phase.

When you are below the boiling point of water (at any pressure) and a temperature _below_ boiling point you could have a gas phase with some water in it (at the water vapour pressure@P. But if there where no other gasses then there would be NO gas phase.

 

[MortenA]

I then asked myself one question: What about steam systems (saturated) where you have steam traps that removes condensate (water)? Well i believe the answer must be that its again a rate process (as with the boiling bot: Eventually (i steam flow was stopped) all the vapour _would_ condense or at least the P would drop to something very close to vacuum.

 

Listen to Boilerman, its good advice. No matter what you calculate, its best to have a method of adjusting the blowdown flow for controlling boilerwater chemistry. In my experience, placing the blowdown valve as close to the flashtank as possible is best. This will also ensure that you´re dealing with single phase flow over the length of the pipe. Hope that helps you out.

 

By considering the intermolecular forces, it can be a region between the molecules which scape from the liquid's surface, and intermolecular forces from liquids surface.
But we can make it easier.
For constant volume (Cv)
and for monoatomic ideal gases with 3 translational degrees of freedom:
Molar specific heat Q = n Cv DeltaT
First law of thermodynamics
DeltaU + P DeltaV = n Cv DeltaT
Because of constant Volume --->>> DeltaV = 0
--->> Cv = (1/n)(DeltaU/DeltaT)
For monoatomic ideal gases
U = (3/2) n R T so Cv = 3/2 R = 12.5 J/mol.K
(By Equipartition of Energy we can colculate the Cv for linear or non linear molecules like water;
U = (s/2) N Kb T = (s/2) n R T and Cv = (s/2) R
where the (s) is degrees of freedom in the molecular motion)
Cp
Q = n Cp DeltaT
P DeltaV = n R DeltaT --->> (DeltaU/DeltaT) + n R = n Cp
Cv = 1/n DeltaU/DeltaT
------->>> Cp = Cv + R
Cp = 5/2 R = 20.8 J/mol.K
Cp/Cv = 1 + (R/s/2R) = 1 + 2/s = (s + 2)/s