The ideal gas equation states that P=nRTV, where P is the pressure, V is the volume, T is the temperature, R = 0.08206 (L.atm/mol.K) is the gas constant, and n is the number of moles. Real gases, especially at higher pressure, deviate from this behavior. Their response can be modeled with the van der Waals equation

where a and b are material constants. Write a script M-file which performs the following for given values of n, a, b and T:

1. creates a vector V, for volume in L, with 10 uniformly distributed random numbers between 1 and 2;
2. sorts the elements of vector V is ascending order to obtain a new vector, named Vs;
3. calculates P twice for each value of Vs, once using the ideal gas equation of state and once with the van der Waals equation of state;
4. using the two sets of values for P, calculates the percentage of error () for each value of Vs;*100%
5. determines and displays the maximum error and the corresponding volume;
6. finally, saves the percentage errors, the maximum error and the corresponding volume variables in a text file named variables. Consider 1 mole of nitrogen gas at 300 K, with a = 1.39 L².atm/mol², and b = 0.0391 L/mol. Use your program to find and display the maximum percent error in P and the corresponding value of the volume. Assign values for n, a, b and T in the Command Window. Make sure that your results are displayed based on Octaves choice among the fixed-point or scientific format with 5 digits.