Gay-Lussac's Law
At constant volume, the pressure of a gas is directly proportional to its absolute temperature. P₁/T₁ = P₂/T₂ for isochoric processes.
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Tire pressure rises ~1 psi per 10°F increase in ambient temperature Pressure cookers reach ~15 psi (121°C) for sterilization Aerosol cans must not be heated; pressure can exceed burst strength Isochoric: W=0, so ΔU = Q = nCvΔT
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Why: Gay-Lussac's law explains tire pressure changes with temperature, pressure cooker behavior, and aerosol can safety.
How: Enter initial pressure and temperature, then final pressure or temperature. The calculator finds the unknown using P₁/T₁ = P₂/T₂.
Run the calculator when you are ready.
🚗 Car Tire in Summer Heat
Tire pressure increase - Initial: 32 psi at 20°C, Final: 50°C
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🍲 Pressure Cooker
Pressure cooker heating - Initial: 1 atm at 20°C, Final: 120°C
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⚠️ Aerosol Can Warning
Aerosol can heating danger - Initial: 1 atm at 25°C, Final: 60°C
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🤿 Scuba Tank in Cold Water
Scuba tank cooling - Initial: 200 bar at 25°C, Final: 5°C
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🏭 Industrial Autoclave
Autoclave sterilization - Initial: 1 bar at 20°C, Final: 121°C
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Input Parameters
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Joseph-Louis Gay-Lussac published the law in 1802, building on Charles's work.
— Gay-Lussac
Always use absolute temperature (Kelvin) in gas law calculations.
— Ideal gas law
For monatomic ideal gas, Cv = 1.5R; for diatomic, Cv = 2.5R.
— Kinetic theory
Combined with Boyle's and Charles's laws gives the ideal gas law PV = nRT.
— Ideal gas law
What is Gay-Lussac's Law?
Gay-Lussac's Law (also known as the Pressure Law) describes the relationship between the pressure and temperature of a gas at constant volume. It states that the absolute pressure of a gas is directly proportional to its absolute temperature when volume and the amount of gas remain constant.
Mathematically, Gay-Lussac's Law is expressed as P₁/T₁ = P₂/T₂, meaning the ratio of pressure to temperature remains constant during an isochoric process. This fundamental law is one of the three gas laws that form the basis of the ideal gas law and is essential in understanding thermodynamic processes.
Key Characteristics:
- Applies to ideal gases at constant volume (isochoric process)
- Pressure and temperature are directly proportional
- The ratio P/T remains constant
- Graphically represented as a straight line on a P-T diagram
- Temperature must be in absolute scale (Kelvin)
- No work is done (W = 0) since volume is constant
- Heat transfer equals internal energy change (Q = ΔU)
Isochoric Processes
Understanding Isochoric Processes
An isochoric process (also called isovolumetric or constant-volume process) is a thermodynamic process in which the volume of the system remains constant throughout. For an ideal gas undergoing an isochoric process, Gay-Lussac's Law applies, and several important thermodynamic relationships hold true.
During an isochoric process:
- Volume is constant: V₁ = V₂
- Pressure is proportional to temperature: P/T = constant
- No work is done: W = 0
- Heat transfer equals internal energy change: Q = ΔU = nCv(T₂-T₁)
- Enthalpy change: ΔH = nCp(T₂-T₁)
- Entropy changes: ΔS = nCv ln(T₂/T₁)
Energy Transfer
In an isochoric heating process, heat is added to the gas, increasing its temperature and pressure. Since no volume change occurs, no work is done, and all the heat energy goes into increasing the internal energy of the gas. In an isochoric cooling process, heat is removed, decreasing temperature and pressure.
The heat transfer can be calculated using: Q = nCv(T₂-T₁), where n is the number of moles and Cv is the heat capacity at constant volume. This equals the change in internal energy: ΔU = Q.
Real-World Applications
Car Tire Pressure
Tire pressure increases with temperature during driving. A tire inflated to 32 psi at 20°C can reach 36-38 psi when heated to 50°C during driving. This is why tire pressure should be checked when tires are cold for accurate measurements.
Pressure Cookers
Pressure cookers work by sealing the lid, keeping volume constant. As the temperature increases during heating, pressure rises dramatically, allowing food to cook at higher temperatures than normal boiling point. This reduces cooking time significantly.
Aerosol Cans
Aerosol cans carry warnings not to expose them to heat because heating increases internal pressure. If the can's volume remains constant, pressure can rise dangerously, potentially causing the can to explode. This is a direct application of Gay-Lussac's Law.
Scuba Diving Tanks
Scuba tanks filled at room temperature experience pressure changes when exposed to cold water. Understanding Gay-Lussac's Law helps divers understand why tank pressure readings may decrease in cold water, even though the amount of gas remains constant.
Industrial Autoclaves
Autoclaves use high pressure and temperature for sterilization. By sealing the chamber (constant volume), heating increases pressure according to Gay-Lussac's Law. This allows sterilization at temperatures above normal boiling point, effectively killing microorganisms.
Automotive Engines
During the compression stroke of an internal combustion engine, the volume decreases, but Gay-Lussac's Law principles help understand pressure-temperature relationships in closed systems. This is important for engine design and performance optimization.
Formula Explanations
Gay-Lussac's Law Equation
The fundamental equation P₁/T₁ = P₂/T₂ states that for a given amount of gas at constant volume, the ratio of absolute pressure to absolute temperature remains constant. This direct relationship means that as temperature increases, pressure increases proportionally, and vice versa.
This law is derived from the kinetic theory of gases and assumes ideal gas behavior. The temperature must be measured on an absolute scale (Kelvin) for the law to hold. At absolute zero (0 K), pressure would theoretically be zero, though real gases would liquefy or solidify before reaching this point.
Work and Energy
For an isochoric process, W = 0 because no volume change occurs. This means no work is done by or on the gas. All energy transfer occurs as heat, and this heat directly changes the internal energy: Q = ΔU = nCv(T₂-T₁).
The enthalpy change for an isochoric process is ΔH = nCp(T₂-T₁), which is different from the internal energy change because enthalpy accounts for the pressure-volume work that would be done if the process were at constant pressure.
Pressure Coefficient
The pressure coefficient β = 1/T represents the fractional change in pressure per unit change in temperature. It shows that the sensitivity of pressure to temperature changes decreases as temperature increases.
This coefficient is important in engineering applications where pressure changes with temperature must be predicted or controlled, such as in sealed containers, pressure vessels, and closed systems.
Limitations and Considerations
Ideal Gas Assumptions
Gay-Lussac's Law applies strictly to ideal gases under specific conditions:
- Gas molecules have negligible volume compared to container volume
- No intermolecular forces between gas molecules
- Perfectly elastic collisions
- Constant volume throughout the process
- No phase changes occur
- Temperature must be measured on absolute scale (Kelvin)
Real Gas Behavior
Real gases deviate from ideal behavior, especially at high pressures and low temperatures. The van der Waals equation or other equations of state may be more appropriate for accurate calculations in these conditions. However, for many practical applications at moderate pressures and temperatures, Gay-Lussac's Law provides excellent approximations.
Safety Considerations
Understanding Gay-Lussac's Law is crucial for safety in many applications. Sealed containers exposed to heat can experience dangerous pressure increases. This is why aerosol cans, propane tanks, and other pressurized containers carry warnings about exposure to heat. Proper pressure relief valves and temperature monitoring are essential safety features.
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