Heat Capacity Question
Heat Capacity Question
(OP)
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
jproj





RE: Heat Capacity Question
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.
RE: Heat Capacity Question
RE: Heat Capacity Question
jproj
RE: Heat Capacity Question
Best Regards
Morten
RE: Heat Capacity Question
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.
RE: Heat Capacity Question
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
RE: Heat Capacity Question
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....
RE: Heat Capacity Question
"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.
RE: Heat Capacity Question
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.
RE: Heat Capacity Question
RE: Heat Capacity Question
RE: Heat Capacity Question
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