How to Calculate and Solve for Coefficient of Thermal Expansion | Fracture
Last Updated on December 15, 2022
The image of coefficient of thermal expansion is represented below.
To compute for coefficient of thermal expansion, three essential parameters are needed and these parameters are Stress (σ), Modulus of Elasticity (E) and Change in Temperature (ΔT).
The formula for calculating coefficient of thermal expansion:
α1 = σ/EΔT
Where:
α1 = Coefficient of Thermal Expansion
σ = Stress
E = Modulus of Elasticity
ΔT = Change in Temperature
Given an example;
Find the coefficient of thermal expansion when the stress is 12, the modulus of elasticity is 8 and the change in temperature is 10.
This implies that;
σ = Stress = 12
E = Modulus of Elasticity = 8
ΔT = Change in Temperature = 10
α1 = σ/EΔT
α1 = 12/(8)(10)
α1 = 12/(80)
α1 = 0.15
Therefore, the coefficient of thermal expansion is 0.15.
Calculating the Stress when the Coefficient of Thermal Expansion, the Modulus of Elasticity and the Change in Temperature is Given.
σ = α1 (EΔT)
Where:
σ = Stress
α1 = Coefficient of Thermal Expansion
E = Modulus of Elasticity
ΔT = Change in Temperature
Let’s solve an example;
Find the stress when the coefficient of thermal expansion is 10, the modulus of elasticity is 5 and the change in temperature is 4.
This implies that;
α1 = Coefficient of Thermal Expansion = 10
E = Modulus of Elasticity = 5
ΔT = Change in Temperature = 4
σ = α1 (EΔT)
σ = 10 (5(4))
σ = 10 (20)
σ = 200
Therefore, the stress is 200.
Calculating the Modulus of Elasticity when the Coefficient of Thermal Expansion, the Stress and the Change in Temperature is Given.
E = σ / α1(ΔT)
Where:
E = Modulus of Elasticity
α1 = Coefficient of Thermal Expansion
σ = Stress
ΔT = Change in Temperature
Let’s solve an example;
Find the modulus of elasticity when the coefficient of thermal expansion is 4, the stress is 48 and change in temperature is 6.
This implies that;
α1 = Coefficient of Thermal Expansion = 4
σ = Stress = 48
ΔT = Change in Temperature = 6
E = σ / α1(ΔT)
E = 48 / 4(6)
E = 48 / 24
E = 2
Therefore, the modulus of elasticity is 2.
Calculating the Change in Temperatute when the Coefficient of Thermal Expansion, the Stress and the Modulus of Elasticity is Given.
ΔT = σ / α1(E)
Where:
ΔT = Change in Temperature
α1 = Coefficient of Thermal Expansion
σ = Stress
E = Modulus of Elasticity
Let’s solve an example;
Find the change in temperature when the coefficient of thermal expansion is 20, the stress is 60 and the modulus of elasticity is 2.
This implies that;
α1 = Coefficient of Thermal Expansion = 20
σ = Stress = 60
E = Modulus of Elasticity = 2
ΔT = σ / α1(E)
ΔT = 60 / 20(2)
ΔT = 60 / 40
ΔT = 1.5
Therefore, the change in temperature is 1.5.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the coefficient of thermal expansion.
To get the answer and workings of the coefficient of thermal expansion using 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 Fracture under Materials and Metallurgical
Now, Click on Coefficient of Thermal Expansion under Fracture
The screenshot below displays the page or activity to enter your values, to get the answer for the coefficient of thermal expansion according to the respective parameter which is the Stress (σ), Modulus of Elasticity (E) and Change in Temperature (ΔT).
Now, enter the values appropriately and accordingly for the parameters as required by the Stress (σ) is 12, Modulus of Elasticity (E) is 8 and Change in Temperature (ΔT) is 10.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the coefficient of thermal expansion and presents the formula, workings and steps too.