# Homework Help: Phase equilibrium with unsteady flow

1. Jul 24, 2008

### fizzybiz

Hi All - I tried this question in Introductory Physics, but thought I'd plonk it here too. Hope that's acceptable.

1. The problem statement, all variables and given/known data

I have an initially closed, pressurised vessel at ambient temperature, with a single species in it at dynamic equilibrium with some volume fraction of vapour and liquid. I am in the "wet vapour" region of the P-v-T surface, described by the Clausius-Clapeyron equation.

I then draw some mass of liquid out. I view the problem in discreet terms, but could possibly model with a mass flow rate out.

In the real world, the vessel will cool - energy will be drawn into the vapour - partially from the effect of vapour expansion (thinking of the liquid rather like a piston in a cylinder) and partially from the effect of vapourisation of some of the remaining liquid. I presume if the mass flow rate is low, the expansion effect will be negligible. I want to quantify the energy flux due to vapourisation.

2. Relevant equations

Clausius-Clapeyron equation, describing vapour pressure at some temperature - the vapour-liquid equilibrium line in the P-T plane. ln(p2/p1) = (dHvap/R)(1/T2 - 1/T1)

Ideal gas law; pV = mRT

(heat flux at constant volume; Q = m.cv.dT; not used)

Possibly use the relative volatility theory described here (http://tinyurl.com/676gsb) for a binary, 2-species problem.

3. The attempt at a solution

I have approached this by first presuming the temperature recovers to ambient at every liquid mass increment drawn from the vessel. I have no model for heat flux across the vessel wall.

I draw mass m of liquid from the tank, then the volume change of vapour is easily calculated from mass/liquid density. I presume if the temperature remains constant that we equilibrate back along the clausius-clapeyron line, and that the vapour pressure remains constant also (not sure if that's valid). Then the new mass of vapour can be found from pV = mRT. The energy flux drawn in to vapourise the mass difference is calculated from Q = dHvap.m.

I'd like to know the volume fractions of vapour and liquid, but I'm not sure if that's useful/misleading.