Source

A note about phases

Pressure

Pression de vapeur saturante Pressure at which the liquid is in equilibrium with its gaz phase. It is the maximal amount of a component that is allowed in a gaz form given the temperature.

Pressure represent the number of molecule around in the given phase.

In an empty room, with (theoretical) pressure of 0, there is no molecule in it. Think to subway, when there is nobody, you feel good, when it is rush hour, you feel pressed.

In this room, adding one kind of molecule or atom (water, alcohool, H2, ...) the pressure will slowly increase.

You will be able to add molecules until reaching the saturation pressure, that represent the maximum number of molecule that can be together in gaz phase.

Reaching this limit, the molecule will condensate to liquid (in most of the case, you can have gaz solid transition). The pressure will stay constant while increasing the amount of liquid. This pressure is call Psat, or saturation pressure.

Two or more components

Maximum is given the Law of Raoult

P = ∑Psatixi

The observed pressure is the sum of the partial pressure, assuming no interaction between components.


Look at isotherme diagrams.

\mu{A,v} = \mu_{A, v}^0(T) + RT \log(\frac{P_{A}}{P^0})
and $ = _{B, v}^0(T) + RT ()

Adding several components leeds to the question: what is the final pressure ? If component A has PsatA < PsatB, what is the final pressure ? The min ? The max ? The mean ?

3 cases, depending on mixibility:

  • Liquid are mixible, with azeotrope
  • Liquid are non mixible, hétéroazéotrope

With 2 components, in liquid form and large excess, the pressure will rise until Psat1 + Psat2.

 Clapeyron

Dupré formula

Allow to get Psat = f(T, P0; a, M, Lv)

\log \left(\frac{P_{sat}}{P_0}\right)= \frac{M L_v}{R} \left(\frac{1}{T_0} - \frac{1}{T} \right) - \frac{M a}{R} \log \left(\frac{T}{T_0}\right)

With:

  • a Factor related to enthalpy
  • Lv Latent Heat of Vaporisation

Approximation for water, given Rankine:

\log p_{sat} = 13.7 - \frac{5120}{T}

For

  • T in Kelvin
  • psat in atmosphere

Humidity

Humidity = 100 \frac{P_{vap}}{P_{sat}}

How far this component is from equilibrium (100%: equilibrium).

Total water in air

The expression "it is very humid today" is relatively frequent, and is associated to the fact that water condensate easily.

However, this doesn't mean that there is a lot of water in the air.

Opening your window to refresh the room air has little effect on humidity on your room, whereas in full summer, you may increase the humidity.

Supposing Water as a perfect Gaz: PV = nRT, quantiy is easily related to saturation pressure.

m = \frac{p_{sat}VM}{nRT}

Temperature (°C) Pressure (mbar) Max water/m3
-60 0.001
-40 0.13
-20
-10
0 6.10
5 8.72
10 12.3
100 1013

After 100°C, we cannot go higher (in an open area) as the gaz will diffuse to lower pressure area. In a closed room, it would be possible to increase the pressure conjointly with the ebullition temperature

This follow an exponential low (until limit temperature of 100°C at normal pressure)