= Entropy of a two-species classical ideal gas
{title2=$Z=Z_1^{N_A+N_B}/(N_A!N_B!)$}
Two physically distinguishable noninteracting species with fixed particle numbers and the same single-particle <partition function> have the displayed <canonical partition function>. If $Z_1\propto VT^{3/2}$, the leading large-particle-number <entropy> is $S=k_B\sum_{i=A,B}N_i[\ln(Z_1/N_i)+5/2]$. With $N=N_A+N_B$ and $x_i=N_i/N$, this equals the one-species expression at total number $N$ plus $-Nk_B\sum_i x_i\ln x_i$. Merely attaching labels to otherwise identical indistinguishable atoms does not justify this mixing term.
Back to article page
