The pressure of a gas and its absolute temperature are directly proportional when the gas volume remains constant.
Understanding the Relationship
Amontons's law, as highlighted in the reference provided, explains this direct relationship. The law specifically states that if the volume of a gas is fixed, then the pressure of the gas increases or decreases in direct relation to its absolute temperature. This means if you double the absolute temperature, you double the pressure, and if you halve the temperature, you halve the pressure. The relationship can be expressed mathematically as:
P ∝ T (where volume and moles are constant)
P/T = k (where 'k' is a constant)
Key Insights
- Direct Proportionality: A direct proportional relationship between pressure and temperature means that as one value increases, the other increases by the same factor.
- Absolute Temperature: The temperature used in this relationship must be absolute temperature, measured in Kelvin (K), which starts from absolute zero (approx. -273.15 °C).
- Constant Volume: This relationship holds true when the volume of the gas remains the same. If the volume changes, the relationship is different.
- Constant Moles: This relationship also holds true when the number of moles of the gas remains the same. If the number of moles changes, the relationship is different.
Practical Examples
Here are a few practical ways you might see this relationship:
- Tire Pressure: When a car tire is heated up from driving, the tire pressure increases because of the increased temperature of the air inside. If you drive on a hot day, your tire pressure will increase faster and more noticeably.
- Pressure Cooker: As a pressure cooker heats up, the temperature increase causes a corresponding rise in the pressure inside, which accelerates the cooking process.
- Aerosol Cans: Aerosol cans can explode when exposed to high temperatures. This is because the heat increases the pressure inside the can, which could exceed the can's capacity to hold the pressure.
Why Absolute Temperature?
Using absolute temperature (Kelvin) is critical for this relationship to work correctly.
- The Kelvin scale starts from absolute zero (0 K), where molecules have minimal energy.
- This starting point ensures that the proportions are consistent and mathematically sound.
Summary Table
| Variable | Proportionality | Condition |
|---|---|---|
| Pressure (P) | Directly | Temperature (T) is absolute |
| Volume (V) is constant | ||
| Moles (n) is constant |
