The Gay-Lussac’s Law Calculator helps you calculate the relationship between pressure and temperature of a fixed amount of gas when the volume remains constant. It’s based on a gas law that shows pressure increases with temperature, provided the gas is in a closed container with a constant volume. This calculator is extremely useful in physics, chemistry, and engineering applications where understanding gas behavior is critical.
By entering values for three known variables (such as initial pressure, initial temperature, and final temperature), you can find the unknown variable (such as final pressure). This saves time and improves accuracy when dealing with real-life gas systems.
This calculator falls under the "Gas Laws Calculator" category.
formula
Gay-Lussac’s Law Formula:
P₁ / T₁ = P₂ / T₂
Rearranged Forms for Calculator Use:
To find final pressure (P₂):
P₂ = (P₁ × T₂) / T₁
To find final temperature (T₂):
T₂ = (T₁ × P₂) / P₁
To find initial pressure (P₁):
P₁ = (P₂ × T₁) / T₂
To find initial temperature (T₁):
T₁ = (T₂ × P₁) / P₂
Where:
P₁ = Initial Pressure (in atm, Pa, bar, etc.)
T₁ = Initial Temperature (in Kelvin only)
P₂ = Final Pressure
T₂ = Final Temperature
Important Note:
Temperatures must always be in Kelvin for these formulas to work correctly.
To convert °C to K:
T(K) = T(°C) + 273.15
Conversion and Reference Table
Here’s a helpful table with commonly searched temperature and pressure conversions. You can refer to this when using the calculator or when doing quick estimations.
| Celsius (°C) | Kelvin (K) | Pressure (atm) | Pressure (Pa) | Pressure (bar) |
|---|---|---|---|---|
| 0 | 273.15 | 1 | 101325 | 1.01325 |
| 25 | 298.15 | 2 | 202650 | 2.0265 |
| 50 | 323.15 | 3 | 303975 | 3.03975 |
| 75 | 348.15 | 4 | 405300 | 4.053 |
| 100 | 373.15 | 5 | 506625 | 5.06625 |
Use this table to convert temperature to Kelvin or to check equivalent pressure units. It can save time when using the calculator or doing quick estimates without needing to convert everything manually.
Example
Let’s go through a simple example to see how the calculator works.
Given:
Initial Pressure (P₁) = 1 atm
Initial Temperature (T₁) = 25°C = 298.15 K
Final Temperature (T₂) = 75°C = 348.15 K
We want to calculate the final pressure (P₂).
Using the formula:
P₂ = (P₁ × T₂) / T₁
P₂ = (1 × 348.15) / 298.15
P₂ ≈ 1.167 atm
So, when you increase the temperature from 25°C to 75°C in a fixed-volume gas container, the pressure increases from 1 atm to about 1.167 atm.
Most Common FAQs
Gay-Lussac’s Law is one of the gas laws that states the pressure of a fixed amount of gas is directly proportional to its temperature (in Kelvin) when the volume is constant. If temperature goes up, pressure goes up, and vice versa.
No, you must convert Celsius to Kelvin before using it. Just add 273.15 to the Celsius temperature to get the Kelvin value.
Yes, Gay-Lussac’s Law is widely used in applications like pressure vessels, cooking under pressure (like pressure cookers), and even in air conditioning systems. It helps engineers design safe and efficient systems involving gases.