The equation of state for a gas is given by the van der Waals equation
where P is the pressure, v is the specific volume, T is the temperature, R is the gas constant, and a, b are constants that depend on the gas. For P = 70 atm, T = 200 K, R = 0.08205 liter atm/mole K, a = 3.59, and b = 0.0427, the specific volume is given in liters/mole. Find this value using the Newton–Raphson method, after obtaining the approximate value by the search method. Also, use the roots function in MATLAB to obtain the solution and compare the result with that obtained earlier.
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