Q. 7.69

Question

(a) As usual when solving a problem on a computer, it's best to start by putting everything in terms of dimensionless variables. So define $t = T / T_{c}$ $c = μ / k T_{c}, and x = ϵ / k T_{c}$ . Express the integral that defines $μ$ , equation 7.122, in terms of these variables. You should obtain the equation

(b) According to Figure 7.33, the correct value of $c$ when $T = 2 T_{c}$ is approximately $- 0.8$ . Plug in these values and check that the equation above is approximately satisfied.

(c) Now vary $μ$ , holding $T$ fixed, to find the precise value of $μ$ for . Repeat for values of $T / T_{c}$ ranging from $1.2$ up to $3.0$ , in increments of $0.2$ . Plot a graph of $μ$ as a function of temperature.