The van der Waals equation of state with a = 0.1368 Pa m³/mol² and b = 3.864 × 10⁻⁵ m³/mol can be used to describe nitrogen.

a. Using the van der Waals equation of state, prepare a graph of pressure (P) of nitogen as a function of log V , where V is molar volume at temperatures of 100 K, 125 K, 150 K, and 175 K. The range of the plot should be V = 1 × 10⁻⁴ to 25 m³/mol. 

b. One mole of nitrogen is to be isothermally compressed from 100 kPa to 10 MPa at 300 K. Determine (1) the molar volume at the initial and final conditions and (2) the amount of work necessary to carry out the isothermal compression. 

c. Repeat the calculation of part (b) for an ideal gas.