(Solved): HW7P4 (18 points) The Redlich-Kwong equation to find the pressure of a gas is as follows where P i ...

HW7P4 (18 points) The Redlich-Kwong equation to find the pressure of a gas is as follows where $$P$$ is the pressure [bar], $$n$$ is the amount of gas [kmol], $$R_u=0.08314\frac{h_{arr}{\mathrm{m}}^3}{\text{ kmbi }{\mathrm{K}}^2}V$$ is volume $$[{\mathrm{m}}^3$$ ], and $$T$$ is the temperature $$[\mathrm{K}]$$. The constants $$c$$ and $$d$$ for air are 15.989 and 0.02541 , respectively. $$P=\frac{R_{\mathrm{u}}T}{\frac{V}{n}?d}?\frac{c}{\frac{V}{n}\left(\frac{V}{n}+d\right)T^{\frac{1}{2}}}$$ The temperature can be determined from the equation as $$T=\frac{P\left(\frac{V}{n}?d\right)}{R_u}+\frac{\frac{c}{R_s}\left(\frac{V}{n}?d\right)}{\frac{V}{n}\left(\frac{V}{n}+d\right)T^{\frac{1}{2}}}$$ Since $$T$$ cannot be isolated, the temperature can, instead, be iteratively determined using the following fixed-point iteration algorithm. Select an initial guess for the temperature, $$T_1=300(\mathrm{N}=1)$$ Update the guess for temperature as $$(\mathrm{N}=2)$$ $$T_2=\frac{P\left(\frac{V}{n}?d\right)}{R_u}+\frac{\frac{c}{R_u}\left(\frac{V}{n}?d\right)}{\frac{V}{n}\left(\frac{V}{n}+d\right)T_1^{\frac{1}{2}}}$$ While $$\left|\frac{T_{i+1}?T_i}{T_i}\right|>10^{?10}$$ and $$N<50$$ Update the guess for temperature as $$T_{i+1}=\frac{P\left(\frac{V}{n}?d\right)}{R_u}+\frac{\frac{c}{R_n}\left(\frac{V}{n}?d\right)}{\frac{V}{n}\left(\frac{V}{n}+d\right)T_i^{\frac{1}{2}}}$$ Write a function file $$[T,N]=$$ Redlich_Kwong $$(\mathrm{P},\mathrm{v},\mathrm{n})$$ - Input arguments: the pressure, $$P$$, volume, $$\mathrm{V}$$, and amount of gas, $$\mathrm{n}$$ as scalars with corresponding units. - Output arguments: the estimated temperature, $$T$$, and the number of guesses/iterations, $$\mathrm{N}$$, it took to estimate the temperature starting at 1.