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 for Solids
For most isotropic solids, the volumetric expansion coefficient is approximately \( \beta \approx 3\alpha \). The table below lists typical values of \( \beta \) for common materials:
| Material | Volumetric Expansion Coefficient \( \beta \) (×10-6/°C) |
|---|---|
| Aluminum | 69 |
| Copper | 51 |
| Iron | 36 |
| Steel (carbon) | 33 |
| Glass (Pyrex) | 9.9 |
| Concrete | 36 |
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 \((\beta \times 10^-5) \color{gray} [\frac{1}{°C} \text{ or } C^{-1}] \color{black}\) |
|---|---|
| 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.
Specific Heat Capacity of Water and Common Liquids
In introductory calorimetry, the specific heat of water is treated as a standard constant. When working in calories, the value used is:
\[ c_{\text{agua}} = 1 \; \frac{\text{cal}}{\text{g·°C}} \]
This value is widely adopted because most exercises use grams, calories, and degrees Celsius. The table below lists typical specific heat capacities of water and other common liquids.
| Liquid | Specific Heat Capacity \( c \) \((\frac{\text{cal}}{\text{g·°C}})\) |
|---|---|
| Water | 1.00 |
| Ethanol | 0.58 |
| Glycerin | 0.60 |
| Mercury | 0.03 |
| Vegetable Oil | 0.50 |
When solving calorimetry problems, use the specific heat value that corresponds to the liquid involved. In SI units, water would instead use:
\[ c_{\text{agua}} = 4186 \; \frac{\text{J}}{\text{kg·K}} \]