The idea behind this thermal expansion calculator is simple: if you heat a material, it expands. If you cool it down, it shrinks. How much though? Well, it depends on the property of the material called the "thermal expansion coefficient". In this article, we explain this concept in more detail. If you want to learn the thermal expansion equation, just keep reading!
What is thermal expansion?
Let's begin with the general idea of thermal expansion: why does it even take place? Every material is composed of molecules stuffed together more or less densely. When we increase the temperature of the material, what we really do is supply energy (if you don't believe it, try the specific heat calculator). Obviously, energy cannot disappear; it just changes its form into kinetic energy (see kinetic energy calculator).
As molecules have higher kinetic energy, they begin to move around more. You can imagine that the more they move, the further away from each other they need to stay. As the separation between molecules increases, the material expands. This expansion can also cause stresses (see thermal stress calculator).
Linear vs. volumetric expansion
Linear expansion is one-dimensional. We typically observe it in all objects for which the length is much longer than the width. Railroad tracks are a good example. Did you notice that the tracks are not continuous but rather made up of hundreds of pieces separated by small spaces (called control joints)? It is because of the thermal expansion. During extreme summers (40 °C), a track can be .048% longer than by 0 °C. It may not seem much, but if a track has a length of 1 km, the difference in length reaches 48 cm! Of course, it doesn't mean that the railroad tracks expand in one direction only; we neglect the increase in height and width, as they are multifold smaller.
Volumetric expansion, on the other hand, is three-dimensional. If a material is isotropic (has the same properties in all directions), it expands uniformly. Let's take a real-life example − opening a closed glass jar with a metal lid. You might find it difficult, but after pouring some hot water on the lid, it gives way more easily. It happens because the lid expands much faster than glass.
There is also a third type of thermal expansion: two-dimensional area expansion. Can you give an example of this phenomenon?
Thermal expansion equation
Our thermal expansion calculator uses a simple formula to find the thermal expansion of any object. The equations for linear and volumetric expansion are very similar.
Linear expansion: ΔL = aL₁(T₂ - T₁)
Volumetric expansion: ΔV = bV₁(T₂ - T₁)
- T₁ – Initial temperature, and T₂ is the final temperature;
- ΔL – Change in object's length;
- L₁ – Initial length;
- a – Linear expansion coefficient;
- ΔV – Change in object's volume;
- V₁ – Initial volume; and
- b – Volumetric expansion coefficient.
Use the thermal expansion calculator to find the change in length or volume – simply type in other values and watch it do all the work for you!
Coefficient of linear expansion
The coefficients of linear and volumetric expansion are rates at which a material expands. For isotropic materials, these two coefficients are related:
b = 3a.
You can find below a list of the most common linear expansion coefficients.
- Aluminum: 22.2×10⁻⁶ / K;
- Concrete: 14.5×10⁻⁶ / K;
- Copper: 16.6×10⁻⁶ / K;
- Glass: 5.9×10⁻⁶ / K;
- Ice: 51×10⁻⁶ / K;
- Silver: 19.5×10⁻⁶ / K;
- Steel: 12.0×10⁻⁶ / K;
- Wood, parallel to grain: 3×10⁻⁶ / K; and
- Wood, across (perpendicular) to grain: 30×10⁻⁶ / K.
What is happening to a substance undergoing thermal expansion?
When an object undergoes thermal expansion, it changes its shape, length, volume, and area in response to a change in temperature. This happens because when an object is heated, the distances between its molecules increase. Consequently, the total mass of the object does not change, but its volume increases and its density decreases.
What is the coefficient of thermal expansion?
The thermal expansion coefficient describes the ability of a specific material to change length (or volume) when heated. Over small temperature ranges, the change in length of a material is proportional to the change in its temperature, and the coefficient of proportionality corresponds to the linear expansion coefficient, a.
There is also a volumetric expansion coefficient (b), which for isotropic materials is equal to b = 3a.
How can I calculate thermal expansion of a steel pipe?
To find the thermal expansion of a steel pipe:
Measure the initial length L₁ of the steel pipe at the initial temperature T₁.
Find the final temperature T₂.
Use linear expansion coefficient for steel, a.
Substitute data into the equation:
ΔL = aL₁(T₂ − T₁)
Measure initial volume V₁ at T₁.
Find the final temperature T₂.
Multiply coefficient a by 3.
Use the formula for volumetric expansion:
ΔV = bV₁(T₂ − T₁)
How much does a 12-meter copper pipe expand when heated by 60 °C?
0.012 m or 1.2 cm. To calculate it easily:
Find the linear expansion coefficient of copper (a): 16.6×10⁻⁶ / K.
Use a formula: ΔL = aL₁(T₂ − T₁), where initial length, L₁ = 12 m, and temperature difference, T₂ − T₁ = 60 °C = 60 K.
Enter your data:
ΔL = 16.6×10⁻⁶ / K × 12 m × 60 K = 0.012 m
How much does a 6-meter steel pipe contract when cooled by 85 °C?
6.12 mm or 0.612 cm. Find the linear expansion coefficient for steel: 12.0×10⁻⁶ / K. Note that the pipe is cooled, so the temperature difference has a negative sign: T₂ − T₁ = -85 °C = -85 K. Finally, use the formula for thermal expansion:
ΔL = aL₁(T₂ − T₁) = 12.0×10⁻⁶ / K × 6 m × (-85°K) = -0.00612 m = -0.612 cm.