Phase : Homogeneous in chemical composition and physical properties.
The place where two kinds of substances meet is called inter facial layer/surface layer/ interface layer.
This is about 10 - 100 Å thick( 3 dimensional). But here we assume it as a 2D layer.
In the above image alpha and beta are two kinds of liquids.
Interactions at the interface differs from that of interactions in substance alpha or beta. Here interactions between alpha and beta molecules is also present where as in alpha only alpha molecules interact with each other and in beta only beta molecules interact with each other.
Therefor interface have a different average molecular energy than that of the separate substances.
Because of this if you change the area of the interface the internal energy of the system changes.
* To increase the area of the interface work must be done on the system.
dw = - PdV + ɣdAdw : Reversible work done on the system
-PdV : Work on the system to increase volume
ɣdA : Additional work
ɣ : Surface tension
dA : Increment in the area of the interface
Force on the piston = P lxlz - ɣlx
ɣlx : force from surface tension
lx : length of the interface on the piston
Pressure on the piston = (P lxlz - ɣlx) / lxlz
= P - (ɣ/lz)
* Surface tension is temperature dependent.
Guggenheim - Katayama equation :
ɣ0 : Constant for each liquid
T : Temperature in Kelvin
Tc : Critical Temperature
n : Empirical factor; 11/9 for organic liquids
Critical Temperature is the highest temperature at which liquid-vapour equilibrium can be observed.
When a 3rd substance is dissolved in the system the ɣ value changes.