Chapter 7.6, Problem 69P

If you have a computer system that can do numerical integrals, it’s not particularly difficult to evaluate $\mu$ for $T>T_c$.

1. As usual when solving a problem on a computer, it’s best to start by putting everything in terms of dimension variables. So define $t=T/T_c$, $c=\mu /k{T}_c$ and $x=\epsilon /k{T}_c$. Express the integral that defines $\mu$, equation 7.122, in terms of these variables. You should obtain the equation

$2.315={\int }_0^{\infty }\frac{\sqrt{x}dx}{e^{\left(x-c\right)/t}-1}$.

1. According to Figure 7.33, the correct value of c when $T=2T_c$ is approximately –0.8. Plug in these values and check that the equation above is approximately satisfied.
2. Now very $\mu$, holding T fixed, to find the precise value of $\mu$
3. for $T=2T_c$. Repeat for values of $T/T_c$ ranging from 1.2 up to 3.0, in increments of 0.2. Plot a graph of $\mu$ as a function of temperature.