# Linear coefficient of thermal expansion

• Nathanael
In summary, the "coefficient of linear expansion" (≡k) is defined as the relationship between the change in length (ΔL) and the change in temperature (ΔT). This definition is an approximation if we treat the Δ's as finite, which is the traditional interpretation. However, the Wikipedia article defines it using the notation for derivatives, suggesting a more precise expression. This could explain why the traditional definition may not always result in the original length when reversed. Additionally, the smallness of the coefficient and its temperature dependence also play a role in this.

#### Nathanael

Homework Helper
The "coefficient of linear expansion" ($≡k$) was defined in my book by the following relationship:
##\Delta L=Lk\Delta T##
Where L is length and T is temperature

I'm wondering, is this just an approximation? Because, if you were to increase the temperature by $\Delta T$ and then calculate the new length, and then decrease the temperature by the same $\Delta T$ and calculate the new length again, you would not get back to your original length.

Wouldn't the "symmetrical" definition of $k$ be
##L_{f}=L_{0}e^{k\Delta T}##

This leads me to the question:
Is the reason they don't define it like this because the idea of 'linear thermal expansion' is not true to that degree of accuracy?
(In other words, finding the new length (to that accuracy) is not as simple as using a single constant?)

Nathanael said:
not as simple as using a single constant?
It's temperature dependent, and generally so small that the dependence isn't measureable before things melt/decompose.

Nathanael said:
The "coefficient of linear expansion" ($≡k$) was defined in my book by the following relationship:
##\Delta L=Lk\Delta T##

That's only an approximation if we treat the $\Delta$'s as finite, which is the traditional interpretation of $\Delta$'s.

I notice the Wikipedia article defines the coefficient of linear expansion using the notation for derivatives. http://en.wikipedia.org/wiki/Thermal_expansion

Stephen Tashi said:
That's only an approximation if we treat the $\Delta$'s as finite, which is the traditional interpretation of $\Delta$'s.

I notice the Wikipedia article defines the coefficient of linear expansion using the notation for derivatives. http://en.wikipedia.org/wiki/Thermal_expansion

Thanks, I didn't see that. Everywhere I looked kept using $\Delta L$ and $\Delta T$. Next time I'll be sure to check Wikipedia.

I think it was very perceptive of you to intuitively realize that it should, more precisely, be expressed differentially.

Chet

• Nathanael

## What is the linear coefficient of thermal expansion?

The linear coefficient of thermal expansion is a measure of how much a material expands or contracts in length when heated or cooled. It is denoted by the symbol α and is usually expressed in units of per degree Celsius (or per degree Kelvin).

## How is the linear coefficient of thermal expansion calculated?

The linear coefficient of thermal expansion is calculated by dividing the change in length of a material by its original length, and then dividing that value by the change in temperature. The resulting value is the linear coefficient of thermal expansion.

## What factors affect the linear coefficient of thermal expansion?

The linear coefficient of thermal expansion is affected by several factors, including the type of material, its crystal structure, and its temperature range. Different materials have different values for their linear coefficient of thermal expansion, and some materials may also have different values depending on the direction of expansion.

## Why is the linear coefficient of thermal expansion important?

The linear coefficient of thermal expansion is important because it helps engineers and scientists understand how materials will behave when exposed to changes in temperature. This information is crucial for designing and constructing structures and devices that can withstand thermal stress and avoid damage or failure.

## How does the linear coefficient of thermal expansion relate to other thermal properties?

The linear coefficient of thermal expansion is related to other thermal properties, such as the thermal conductivity and specific heat capacity, in that they all describe how a material responds to changes in temperature. However, the linear coefficient of thermal expansion specifically measures the change in length of a material, whereas the other properties measure different aspects of heat transfer and storage.