This all-in-one online Linear Thermal Expansion Calculator performs calculations using a formula that relates the initial temperature (T1), final temperature (T2), the initial length of an object (L1), and the coefficient (αt) of linear thermal expansion with the change in length ΔL of that object. You can enter the values of any four parameters in the fields of this calculator and find the missing parameter.
ΔL = αt · L1 · (T2 – T1)
Linear Thermal Expansion
Thermal expansion is the tendency of matter to change its dimensions, area, and volume in response to a change in temperature. When a material is heated, its particles begin to move faster and tend to occupy more space, causing the material to expand. Conversely, cooling a material generally results in contraction. This phenomenon is particularly important in engineering, construction, manufacturing, and a range of scientific applications, where dimensional changes due to temperature must be accounted for.
While thermal expansion occurs in three dimensions, linear thermal expansion refers specifically to the change in length of an object when its temperature changes, assuming the expansion in the other dimensions is negligible or not critical for the context.
When is linear thermal expansion important?
Linear thermal expansion becomes the primary consideration when the change in length is the most relevant dimension affected by temperature. This often applies to long, narrow objects such as rods, beams, rails, wires, or structural components. In such cases, expansion in width or thickness is relatively small and often disregarded in calculations or design.
Linear expansion is typically considered in solids, where the shape and structure of the material remain largely intact despite thermal changes.
The Linear Thermal Expansion Equation
The relationship between the change in length of an object and the temperature change it undergoes is given by the linear thermal expansion equation:
$$ \Delta L = \alpha_t \cdot L_1 \cdot (T_2 – T_1)$$
where:
• \(\Delta L\) is the change in length of an object,
• \(\alpha_t\) is the coefficient of linear expansion (per °C or per °K or per °F),
• \(L_1\) is the original length of the object,
• \(T_1\) is the initial temperature of the object,
• \(T_2\) is the final temperature of the object.
This formula assumes a uniform material and a moderate temperature range, over which the coefficient of expansion remains constant.
Example
Suppose we have a steel rod that is 2 meters long, and the temperature increases from 0°C to 30°C. Given that the coefficient of linear expansion of steel is approximately 12 × 10-6 /°C, using our Linear Thermal Expansion Calculator we can easily find that the increase in length will be 0.00072 meters or 0.72 mm.
Coefficient of Linear Expansion
The coefficient of linear thermal expansion, often denoted by \(\alpha_t\), is a material-specific constant that quantifies how much a material expands per unit length for each degree of temperature change.
It has units of 1/°C (or 1/K, since the Celsius and Kelvin scales have the same step size), or 1/°F, and its value depends on the atomic structure and bonding of the material. Generally, metals have higher coefficients of expansion compared to ceramics or composites.
Here are typical values of thermal expansion coefficients for some common materials:
Materials with very low coefficients are used in precision engineering tools and scientific instruments, as they experience minimal expansion or contraction with temperature changes.
It’s important to note that the coefficient of linear expansion can vary slightly with temperature, especially for polymers or composites. For most practical engineering applications, however, a constant average value is used within the relevant temperature range.
Negative Thermal Expansion
While most materials expand when heated, some exhibit negative thermal expansion — they contract as temperature increases. This occurs in certain ceramics and complex materials like zirconium tungstate (ZrW2O8) due to unique atomic bonding and structural flexibility.
A familiar example is ice near its melting point: as ice warms toward 0°C, it contracts slightly because its open crystalline structure begins to collapse. This unusual water behavior explains why ice floats, which in turn defines the important role of ice in insulating aquatic ecosystems in cold conditions.
In case of negative thermal expansion, the coefficient of thermal expansion obviously has negative values.
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