Question

Use a computer to reproduce Table 3.2 and the associated graphs of entropy, temperature, heat capacity, and magnetization. (The graphs in this section are actually drawn from the analytic formulas derived below, so your numerical graphs won't be quite as smooth.)

Short answer

Table 3.2 can be reproduced by using a computer as follows:

The graphs can also be made as:

Step-by-step solution

Given Information

Table 3.2 showing the thermodynamic properties of a two-state paramagnet consisting of 100 elementary dipoles is given as follows:

$N=100dipoles$

Calculation

The table values are calculated with the help of the following formulae:

$N=\left(N_{\downarrow }+N_{\uparrow }\right)$

$U=\mu B\left(N_{\downarrow }-N_{\uparrow }\right)$

$M=\mu \left(N_{\downarrow }-N_{\uparrow }\right)=-\frac{U}{B}$

$\mathrm{\Omega }=\frac{N!}{N_{\downarrow }!(N-N_{\downarrow })!}=\frac{N!}{N_{!}!N_{\downarrow }!}$

$T=\frac{\Delta U}{\Delta S}$

$C=\frac{\Delta U}{\Delta T}$

The table can be computed as follows:

Also,

The graphs are computed as follows:

Entropy as a function of energy for a two-state paramagnetic material can be made as:

The graph of Temperature as a function of energy can be made as:

Graph of Heat capacity can be made as:

Graph of magnetization can be made as:

Final answer

The table is reconstructed as:

The graphs are made based on the table values as: