How to Calculate and Solve for Chapman Enskog Theory Integral | Transport Phenomena
Last Updated on May 14, 2024
The image above represents Chapman Enskog theory integral. To calculate Chapman Enskog theory integral, three essential parameters are needed and these parameters are Boltzmann’s Constant (KB), Temperature (T) and Enskog Constant (Energy Parameter) (ε).
The formula for calculating Chapman Enskog theory integral:
ηn = KBT / ε
Where:
ηn = Chapman Enskog Theory Integral
KB = Boltzmann’s Constant
T = Temperature
ε = Enskog Constant (Energy Parameter)
Let’s solve an example;
Find the Chapman Enskog theory integral when the Boltzmann constant is 1.380e-23, the temperature is 20, and the Enskog constant (energy parameter) is 10.
This implies that;
KB = Boltzmann’s Constant = 1.380e-23
T = Temperature = 20
ε = Enskog Constant (Energy Parameter) = 10
ηn = KBT / ε
So, ηn = (1.380e-23)(20) / 10
ηn = 2.76129e-22 / 10
ηn = 2.76e-23
Therefore, the Chapman Enskog theory integral is 2.76e-23.
Calculating the Temperature when the Chapman Enskog Theory Integral, the Boltzmann’s Constant and the Enskog Constant (Energy Parameter) are Given
T = ηn x ε / KB
Where:
T = Temperature
ηn = Chapman Enskog Theory Integral
KB = Boltzmann’s Constant
ε = Enskog Constant (Energy Parameter)
Let’s solve an example;
Find the temperature when the Chapman Enskog theory integral is 10, the Boltzmann’s constant is 1.380e-23 and the Enskog constant (energy parameter) is 8.
This implies that;
ηn = Chapman Enskog Theory Integral = 10
KB = Boltzmann’s Constant = 1.380e-23
ε = Enskog Constant (Energy Parameter) = 8
T = ηn x ε / KB
T = 10 x 8 / 1.380e-23
So, T = 80 / 1.380e-23
T = 5.79e+24
Therefore, the temperature is 5.79e+24.
Read more: How to Calculate and Solve for Stefan Boltzmann’s Constant | Radiation Heat Transfer
Calculating the Enskog Constant (Energy Parameter) when the Chapman Enskog Theory Integral, the Temperature and the Boltzmann’s Constant are Given
ε = ηn x T / KB
Where:
ε = Enskog Constant (Energy Parameter)
ηn = Chapman Enskog Theory Integral
KB = Boltzmann’s Constant
T = Temperature
Let’s solve an example;
Find the Enskog constant (energy parameter) when the Chapman Enskog theory integral is 20, the Boltzmann’s constant is 1.380e-23 and the temperature is 10.
This implies that;
ηn = Chapman Enskog Theory Integral = 20
KB = Boltzmann’s Constant = 1.380e-23
T = Temperature = 10
ε = ηn x T / KB
That is, ε = 20 x 10 / 1.380e-23
ε = 200 / 1.380e-23
ε = 1.44e+25
Therefore, the enskog constant is 1.44e+25.
How to Calculate Chapman Enskog Theory Integral Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the Chapman Enskog theory integral.
To get the answer and workings of the Chapman Enskog theory integral, use the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.
Now, Click on Transport Phenomena under Materials and Metallurgical
Now, Click on Chapman Enskog Theory Integral under Transport Phenomena
The screenshot below displays the page or activity to enter your values, to get the answer for the chapman enskog theory integral according to the respective parameter which is the Boltzmann’s Constant (KB), Temperature (T) and Enskog Constant (Energy Parameter) (ε).
Now, enter the values appropriately and accordingly for the parameters as required by the Boltzmann’s Constant (KB) is 1.380e-23, Temperature (T) is 20 and Enskog Constant (Energy Parameter) (ε) is 10.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the chapman enskog theory integral and presents the formula, workings and steps too.
