The Relationship Between Pressure, Temperature, and Volume
The pressure of a gas in a rigid vessel is directly proportional to its absolute temperature. This is described by Gay-Lussac's Law:
* P₁/T₁ = P₂/T₂
Where:
* P₁ = Initial pressure
* T₁ = Initial temperature (in Kelvin)
* P₂ = Final pressure
* T₂ = Final temperature (in Kelvin)
Calculating Pressure Change
To calculate the pressure decrease for a 1°C temperature decrease, you need to follow these steps:
1. Convert temperatures to Kelvin: Add 273.15 to your Celsius temperatures.
2. Determine the initial and final pressures: You'll need to know the initial pressure (P₁) to calculate the final pressure (P₂) after the temperature decrease.
3. Apply Gay-Lussac's Law: Solve the equation for P₂.
Example:
Let's say:
* Initial pressure (P₁) = 1 atm
* Initial temperature (T₁) = 20°C = 293.15 K
* Temperature decrease = 1°C
* Final temperature (T₂) = 19°C = 292.15 K
Using Gay-Lussac's Law:
* (1 atm / 293.15 K) = (P₂ / 292.15 K)
* P₂ = (1 atm * 292.15 K) / 293.15 K
* P₂ ≈ 0.9965 atm
Pressure decrease: 1 atm - 0.9965 atm = 0.0035 atm
Conclusion
The pressure decrease for a 1°C temperature decrease depends on the initial pressure and temperature. It's not a fixed value. You need to use Gay-Lussac's Law to calculate the specific pressure change based on the initial conditions.
