# Compression power equation of a gas mixture

1. Oct 29, 2012

### streamlinerr

1. The problem statement, all variables and given/known data
I have a mixture of hydrogen (H2) and water (vapor) that is compressed from pressure p1 to p2. Mass flow of the mixture is known, as well as mass fraction of the hydrogen in the mixture.

Known data:
Pressure p1
Pressure p2
Temperature T
mass flow Mf
mass fraction wH2

I need to develop an equation for the power of a compressor as a function of the above data.

2. Relevant equations

Equation of state in the form of:
p = ρ * R * T

with ρ being the density and R a specific gas constant

3. The attempt at a solution
At first I thought this should be easy, however I stumbled on a problem pretty quickly.

In the adiabatic compressor power equation we have a volume flow Q, which is a mass flow Mf divided by density ρ. I tried developing an equation for the density of a mixture from an equation of state:

ρ = p/T * 1/R

Since mixture density is a combination of both densities i thought to calculate the mixture density the following way:
ρmixt = ρH2 * wH2 + ρH2O * (1-wH2) = p/T * ( wH2 / RH2 + (1-wH2) / RH2O)

with RH2 and RH2O being the specific gas constants of hydrogen and water vapor.

I'm not sure if this the correct way to calculate the mixture density. Is the use mass fraction correct or should i use volume fraction?

Second problem arises when trying to determine heat capacity ratio γ that appears in the compression equation. I've been looking how to determine γ of a mixture (as a function of properties given above), but failed so far.

I'd appreciate some help on this issue.

Thanks.