Apply the secant method to find the molar volume of the methane at $40$ bar and $100C.$ Using the Ping Robinson equation.

$p=\frac{RT}{V-b}-\frac{a}{V(V+b)+b(V-b)}$

$a=0\mathrm{.}45724\frac{R^2{T}_c^2}{p_c}$

$b=0\mathrm{.}07780\frac{R{T}_c}{p_c}$

$=[1+m(1-\sqrt[\phantom{2}]{T_r}){]}^2$

$m=0\mathrm{.}379642+1\mathrm{.}48503-0\mathrm{.}1644{}^2+0\mathrm{.}016667{}^3$