# Liquid condensing out in thermodynamics

1. Mar 10, 2006

### sachi

We have the following expression for the temperature of the latent heat of vaporisation:

d(L/T)/dT = (Cpv - Cpl)/T + [d(Vv - Vl)/dT] *dP/dT

Where Cpv is the heat capacity at constant pressure of the vapour and the liquid respectively, Vv and Vl are the volumes of the vapour and liquid respectively, and the d(Vv - Vl)/dT is a partial derivative at constant P.

We need to show that "when the saturated vapour of an incompressible liquid is expanded adiabatically, some liquid condenses out if Cpl + Td(L/T)/dT < 0"

I'm not sure about the meaning of "saturated vapour". Does this mean it is in equilibrium with the liquid (i.e we are on the phase boundary in the P-T plane), or does it mean supersaturated (i.e there is no liquid present)?
Also, what significance does "incompressible liquid" have?
thanks very much for your help.

2. Mar 10, 2006

### Cyrus

saturated vapor means the quality is equal to exactly 1. So yes, you are correct, it is on the edge of the P-T diagram where it is all vapor, but any slight change and it will go back down to saturated (i.e. some liquid and vapor) or go up into superheated.

Incompressible means Cp=Cv.

3. Mar 10, 2006

### sachi

i'm still a little unsure as to how the piece of info Cp=Cv relates to this question. It's doesn't seem to be necessary to solve the problem.

4. Mar 10, 2006

### Cyrus

Perhaps you do not need it, I was just answering your question as to what is the significance of incompressible liquid. Also, the density of the liquid remains a constant. The density will not change with pressure, it will be highly dependent on temperature.