Thermal Expansion & Heat Coefficients
Linear Thermal Expansion
The coefficient of linear thermal expansion \( \alpha \) quantifies how much a material expands or contracts when its temperature changes.
- \( \Delta L \) — 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 Solids
| Material | \( \alpha \) (×10-6 /°C) |
|---|---|
| Aluminum | 23 |
| Copper | 17 |
| Iron | 12 |
| Steel (carbon) | 11 |
| Glass (Pyrex) | 3.3 |
| Concrete | 12 |
Volumetric Thermal Expansion
The coefficient of volumetric thermal expansion \( \beta \) indicates how much the volume of a material changes with temperature.
For isotropic solids, \( \beta \approx 3\alpha \). For liquids, \( \beta \) must be obtained from experimental tables.
Solids
| Material | \( \beta \) (×10-6 /°C) |
|---|---|
| Aluminum | 69 |
| Copper | 51 |
| Iron | 36 |
| Steel (carbon) | 33 |
| Glass (Pyrex) | 9.9 |
| Concrete | 36 |
Liquids
| Liquid | \( \beta \) (×10-5 /°C) |
|---|---|
| Ethanol | 75 |
| Water (20 °C) | 21 |
| Glycerin | 49 |
| Gasoline | 95 |
| Mercury | 18 |
Example: \( \beta_{\text{ethanol}} = 75 \times 10^{-5} \, ^\circ\text{C}^{-1} \)
Specific Heat Capacity
In introductory calorimetry, the specific heat of water is treated as a standard constant. When working in calories:
Common Liquids
| Liquid | \( c \) (cal / g·°C) | \( c \) (J / kg·K) |
|---|---|---|
| Water | 1.00 | 4186 |
| Ethanol | 0.58 | 2428 |
| Glycerin | 0.60 | 2512 |
| Mercury | 0.03 | 126 |
| Vegetable Oil | 0.50 | 2093 |
| Aluminum | 0.215 | 900 |
Latent Heat
Latent heat is the energy absorbed or released during a phase transition at constant temperature. There are two types:
- Heat of fusion \( L_f \): solid ↔ liquid
- Heat of vaporization \( L_v \): liquid ↔ gas
Water / Ice
| Transition | \( L \) (cal / g) | \( L \) (kJ / kg) |
|---|---|---|
| Fusion (ice → water, 0 °C) | 80 | 334 |
| Vaporization (water → steam, 100 °C) | 540 | 2260 |