Thermal expansion coefficient calculation — where is my mistake?

In summary, the problem that was encountered in calculating the thermal expansion coefficient was due to incorrect units. The specific volume needs to be expressed in m^3/mol instead of m^3/kg in order for the calculation to be accurate. Multiplying the specific volume by the molar mass of the substance will result in the correct units and the equation will work properly.
  • #1
ReuvenD10
9
1
Homework Statement
Get values of thermal expansion coefficient
Relevant Equations
below
Hello everyone,
Once I got through the VDW state equation I came to the expression of the thermal expansion coefficient. When I place the values I get an illogical answer. Is there a problem with the units? (Please ignore the values)

Thanks.

1611562286615.png


This is the unit equation I get to and get stuck:
1611562244596.png
 

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  • #2
You need to use a value of v in m3/mol.
 
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  • #3
ReuvenD10 said:
Homework Statement:: Get values of thermal expansion coefficient
Relevant Equations:: below

Hello everyone,
Once I got through the VDW state equation I came to the expression of the thermal expansion coefficient. When I place the values I get an illogical answer. Is there a problem with the units? (Please ignore the values)

Thanks.

View attachment 276808

This is the unit equation I get to and get stuck:
View attachment 276807
That specific volume (##m^3/Kg##) would be compatible to be used in the members of summation of the denominator of that equation only if multiplied by the molar mass of the specific substance (##Kg/mol##); therefore, the units of v should be expressed in ##m^3/mol##, rather than ##m^3/Kg##.
The units of each member of summation of the denominator would then be Joule/mol.
 
  • #4
thanks. it work.
 
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Likes Lnewqban

1. What is the thermal expansion coefficient?

The thermal expansion coefficient, also known as the coefficient of thermal expansion (CTE), is a measure of how much a material expands or contracts when its temperature changes. It is typically expressed in units of per degree Celsius (or per Kelvin) and is an important factor in the design and engineering of various materials and structures.

2. How is the thermal expansion coefficient calculated?

The thermal expansion coefficient is calculated by taking the change in length, volume, or area of a material divided by its original length, volume, or area, multiplied by the change in temperature. This can be expressed mathematically as: CTE = (ΔL/L) / ΔT or CTE = (ΔV/V) / ΔT or CTE = (ΔA/A) / ΔT, depending on the specific application.

3. What are some common mistakes when calculating the thermal expansion coefficient?

Some common mistakes when calculating the thermal expansion coefficient include using incorrect units for temperature, using the wrong formula for the specific application, or not accounting for the original length, volume, or area of the material. It is important to double check all units and formulas to ensure an accurate calculation.

4. Can the thermal expansion coefficient change with temperature?

Yes, the thermal expansion coefficient can change with temperature. In fact, it is often necessary to use a different thermal expansion coefficient for different temperature ranges in order to accurately predict the expansion or contraction of a material. This is known as the average coefficient of thermal expansion.

5. How is the thermal expansion coefficient used in real-world applications?

The thermal expansion coefficient is used in a variety of real-world applications, such as in the design of bridges and buildings to account for temperature changes, in the manufacturing of electronic components to ensure proper fit, and in the production of glass and ceramics to prevent cracking from temperature fluctuations. It is also an important consideration in materials selection for various industries, such as aerospace and automotive, to ensure the durability and reliability of products.

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