Use mathematical software, a spreadsheet, or the Living graphs on the web site for this book to: 

(a) Evaluate the change in entropy of 1.00mol CO₂(g) on expansion from 0.001m³ to 0.010m³ at 298K, treated as a van der Waals gas.

(b) Allow for the temperature dependence of the heat capacity by writing C=a+bT+c/T², and plot the change in entropy for different values of the three coefficients (including negative values of c).

(c) Show how the first derivative of G, (∂G/∂p)_T, varies with pressure, and plot the resulting expression over a pressure range. What is the physical significance of (∂G/∂p)_T?

(d) Evaluate the fugacity coefficient as a function of the reduced volume of a van der Waals gas and plot the outcome for a selection of reduced temperatures over the range 0.8≤V_r≤3.