Thermal Expansion Coefficient
The coefficient of linear thermal expansion \( \alpha \) quantifies how much a material expands or contracts when its temperature changes.
\[ \Delta L = \alpha L_0 \Delta T \]
where:
- \( \Delta L \) = change in length (m)
- \( L_0 \) = original length (m)
- \( \Delta T \) = temperature change (°C or K)
- \( \alpha \) = linear expansion coefficient (1/°C)
Typical Values for Common Materials
| Material | Coefficient of Linear Expansion \( \alpha \) (×10-6 /°C) |
|---|---|
| Aluminum | 23 |
| Copper | 17 |
| Iron | 12 |
| Steel (carbon) | 11 |
| Glass (Pyrex) | 3.3 |
| Concrete | 12 |
For volumetric expansion, the formula is:
\[ \Delta V = \beta V_0 \Delta T \]
where \( \beta \approx 3\alpha \) for isotropic solids.
Volumetric Expansion Coefficients
The coefficient of volumetric thermal expansion \( \beta \) indicates how much the volume of a material changes with temperature. For liquids, \( \beta \) is typically much larger than for solids.
\[ \Delta V = \beta V_0 \Delta T \]
In most solids, \( \beta \approx 3\alpha \), but for liquids the value must be obtained from experimental tables.
Typical Volumetric Expansion Coefficients for Liquids
| Liquid | Volumetric Expansion Coefficient \( \beta \) (×10-5 /°C) |
|---|---|
| Ethanol | 75 |
| Water (20 °C) | 21 |
| Glycerin | 49 |
| Gasoline | 95 |
| Mercury | 18 |
For example, in thermal expansion problems involving ethanol, the value used is \( \beta_{\text{etanol}} = 75 \times 10^{-5} \, ^\circ\text{C}^{-1} \), taken from standard physics reference tables.