5.17. The equation of state for a gas is given by the van der Waals equation \left(P+\frac{a}{v^{2}}\right)(v-b)=R T 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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5.17. The equation of state for a gas is given by the van der Waals equation \left(P+\frac{a}{v^{2}}\right)(v-b)=R T 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.