Equations of state are used to model the pressure, specific volume, and temperature behavior of a particular gas. One of the oldest equations of state is the van der Waals equation, which is described by Equation 1, where R is the ideal gas constant [kJ/kg/K], T is the temperature [K], v is the specific volume [m^3/kg], and P is the pressure [kPa]. P = RT/v - b - a/v^2 The constant b corrects for the volume occupied by the molecules, and a/v^2 corrects for the intermolecular forces of attraction. The constants a and b can be calculated using the relationships below, where R is the ideal gas constant [kJ/kg/K], T_c is the critical temperature [K], and P_c is the critical pressure [kPa]. a = 27/64 R^2 T^2_c/P_c b = RT_c/8P_c If constants a and b are set to zero, Equation 1 reduces to the Ideal Gas Law shown in Equation 2. P = RT/v (a) Create a MATLAB function to model the pressure of a gas (P) as a function of specific volume v and temperature T. The function should take four input arguments: 1) a numeric input for specific volume, 2) a numeric input for temperature, 3) a string specifying the name of the gas, and 4) a string specifying whether the van der Waal or ideal gas model should be used. The function should return the calculated pressure. The function should correctly assign the gas constant (R), critical temperature (T_c), and critical pressure (P_c) for oxygen, nitrogen, and carbon dioxide, which are provided in Table 1. As an example, the function call might look like: pressure = eqofstate(v, T, 'oxygen', 'vanderWaals') (b) Create a script to call the function created in part (a). The script should calculate the pressures for carbon dioxide at 273 K, and a specific volume range from 0.012 m^3/kg to 0.03 m^3/kg. Plot the pressure vs. specific volume relationship for both the Ideal Gas and van der Waals equation on the same plot