An Introduction to Thermal Physics · Problem 2.37

The Second Law — Daniel Schroeder

Physics — Statistical Mechanics · entropy-of-mixing

Problem

Using the same method as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases,

A

and

B

, whose relative proportion is arbitrary. Let

N

be the total number of molecules and let

x

be the fraction of these that are of species

B

. You should find

\Delta S_{\text{mixing}} = -Nk\left[x \ln x + (1-x)\ln(1-x)\right].

Check that this expression reduces to the one given in the text when

x = 1/2