Calculating the Fraction of Steam in a Mixture

Question

I have a stream ($10,000$ $m^3/d$) of inert gas and steam. The temperature of the stream is $195$ $^oC$, and the absolute pressure is $1455$ $kPa$.

I am trying to find the amount of steam that can be present in the system. I can assume $100\%$ quality saturated steam.

Would I be correct in approximating the steam fraction to be: $P_{sat@T}$ / $P_{stream}$

At $195$ $^oC$, the $P_{sat}$ of steam is $1398$ $kPa$. Therefore the fraction of steam is: $1398/1455$ $=$ $96\%$.

I can then find the volume of steam: $0.96*10,000$ $=$ $9,600$ $m^3/d$.

Is my reasoning correct. Any other ways to calculate this question?

Answer 1

If the saturation pressure at $195^\circ C$ is $1398 kPa$, and you're above this pressure, technically you have compressed liquid water. Never the less, we'll assume you have 100% quality saturated steam for a moment.

The Gibbs phase rule says that $f=C-P+2$, where $f$ is the number of degrees of freedom, $C$ is the number of components in the system (two in your case, inert gas and steam), and $P$ is the number of phases (one in your case, everything is vapor phase). This means you have 3 total degrees of freedom. However, you only specified two (pressure, temperature), so the third (mass fraction of steam or inert gas) remains unspecified. Unfortunately, you cannot determine the steam content with the given information alone.

I think you were hinting at the concept of partial pressures with the calculation you showed. Unfortunately, you don't know the partial pressure or the mass fraction of the steam, so this doesn't help much either.