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Chapter 3

Chapter 3#

Question #11: CoolProp vs. Ideal Gas#

Consider air at atmospheric pressure and room temperature. Calculate the density of air based on:

a) ideal gas law

b) CoolProp module

c) calculate error percentage

d) consider decreasig the temperature of air to \(T_c=85K\) in constant pressure. Calculate and plot the error percentage in calculating density using ideal gas assumption for this temperature range.

Solution Approach for a)#

from ideal gas law,

\(Pv=RT\)

and \(D=1/v\)

so

\(D=P/RT\)

#define variables
T = 25 + 273.15   #room temperature in K
P = 101325   #atmospheric pressure in Pa
R = 287   #air gas constant in J/kg.K

D_ideal = P / (R * T)   #gas density in kg/m3

print('The density of air based on ideal gas assumption is:', f"{D_ideal:.3f}", 'kg/m3')

The density of air based on ideal gas assumption is: 1.184 kg/m3

Solution Approach for b)#

#import library
import CoolProp.CoolProp as CP
fluid = "air"  # define the fluid or material of interest

D_CoolProp = CP.PropsSI("D", "P", P, "T", T , fluid)

print('The density of air based on CoolProp is:', f"{D_CoolProp:.3f}", 'kg/m3')

The density of air based on CoolProp is: 1.184 kg/m3

Solution Approach for c)#

The error percentage is based on the difference in density and the CoolProp result which is based on experiments

\(E=100\times (|D_{CoolProp}-D_{ideal}|)/D_{CoolProp}\)

#import library
import numpy as np
E = 100 * np.absolute(D_CoolProp-D_ideal)/D_CoolProp   #error percentage

print('The error percentage in calculating density is:', f"{E:.3f}", '%')

The error percentage in calculating density is: 0.016 %

Solution Approach for d)#

#import library
import matplotlib.pyplot as plt

T_c = 85   #minimum temperature in K

T_vals = np.linspace(T_c, T, 1000)    #an array for temperatures
E = np.zeros(1000)   #empty array to store error values

i = 0   #counter for the for loop
for T in T_vals:
    D_ideal = P / (R * T)   #gas density using ideal gas assumption in kg/m3
    D_CoolProp = CP.PropsSI("D", "P", P, "T", T , fluid)    #gas density using CoolProp in kg/m3
    E[i] = 100 * np.absolute(D_CoolProp-D_ideal)/D_CoolProp   #error percentage
    i = i +1

plt.plot(T_vals,E)
plt.ylabel("Error [%]")  # give y axis a label
plt.xlabel("Temperature [K]")  # give x axis a label

Text(0.5, 0, 'Temperature [K]')
../../_images/93a8eb3cb307ea81acbac59440661d6870a5697446c6aa4ec321cb0c69a7691d.png
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