# Imagine that particles interact in pairs. If the interaction energy of two particles is 2ε,…

Imagine that particles interact in pairs. If the interaction energy of two particles is 2ε, then half of that (ε) can be associated with each particle. Let εA, εB, εX represent the interaction energy per particle for pairs of As, Bs, and unlike particles, respectively. (For attractive interactions, these energies are negative.) There are N f particles of type B and N(1 − f ) of type A.

(a) Show that the change in potential energy (equal and opposite to the change in thermal energy) is given by

(b) In the common case where attraction between like particles is stronger than that between unlike particles, 2εX − εA − εB > 0, so the answer to part (a) is positive. Potential energy rises and thermal energy falls, and the answer to (a) represents energy that must be added to the system to keep its temperature constant. As can be seen, ∆G = −T ∆Sm − T ∆Si must be concave upward everywhere to avoid a solubility gap. What restriction does this place on the factor 2εX − εA − εB for any value of f?

### Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper Now

(c) Suppose that εA = εB = −0.25 eV and εX = −0.20 eV. At what temperature would A and B be miscible for all f ?

### Looking for a Similar Assignment? Let us take care of your classwork while you enjoy your free time! All papers are written from scratch and are 100% Original. Try us today! Use Code FREE15 