Lab $3$: Equations of State

Overview:

An Equations of State $($EOS$)$ is a mathematical relation between the pressure, volume,

temperature, and number of moles of a fluid $($liquid or gas$).$ In engineering thermodynamics, EOS

is a useful modeling tool to study the phase behavior of liquids and gases and plot the phase

diagrams of fluids during phase changes. One of the commonly used EOS which is cubic in volume

is the van der Waals $($vdW$)$ EOS. It is a pressure explicit equation and has the following form in

molar basis:

$(P+\frac{a}{V^2})(v-b)=RT$

where

$a=\frac{27}{64}(\frac{R^2{T}_C^2}{P_C})$

and

$b=\frac{RTc}{8P_C}$

The variables are defined by:

$P=$ pressure in atm

$V=$ molar volume in $\frac{L}{g}$mol

$T=$ temperature in $K$

$R=$ gas constant $(R=0\mathrm{.}08206$atm$\frac{L}{g}$mol$)$

$Tc=$ critical temperature in $K$

$Pc=$ critical pressure in atm

Pr reduced pressure, $Pr=\frac{P}{P}c$

$Z=$ the compressibility factor, $Z=P\frac{V}{R}T$

It is important to calculate molar volume of fluids at various pressures and constant temperature.

With the given information above:

a$-$ Write the algorithm for the calculation of molar volume and compressibility factor at

various pressure and constant temperature $($pressure and temperature are input data$).$

b$-$ Sketch the flow chart for the calculation of volume and compressibility factor at various

pressure and constant temperature $($pressure and temperature are input data$).$

c$-$ Write a script to calculate molar volume and compressibility factor for gaseous ammonia

at a pressure P$=56$ atm and a temperature T$=450$ K using the vdW EOS $($Tc and Pc for

gaseous ammonia are given below$).$

d$-$ Write a script to calculate molar volume and compressibility factor of gaseous ammonia at

the reduced pressures ranging from $1$ to $20$ by increment of $1$ with the Tc and Pc given

below.

e$-$ Using the disp command to generate a table with the pressure as the first column, molar

volume as the second column and the compressibility factor as the third column.

f$-$ Use the plot command to plot the variation of the compressibility factor versus pressure at

constant temperature of $450$ K$.$ Label the y and x axes with standard title and legend.

For gaseous ammonia Tc$=405\mathrm{.}5$ K and Pc$=111\mathrm{.}3$ atm