1.5
contextual
0.00333333
atm/K
1.5
x
50
%
1.5
contextual
0.00333333
atm/K
1.5
x
50
%
Gay-Lussac's Law Calculator determines the relationship between gas pressure and absolute temperature at constant volume: P₁/T₁ = P₂/T₂. Enter the initial pressure and temperature, then provide the final temperature to find the final pressure, or vice versa. This law explains why pressure cookers work, why aerosol cans are dangerous when heated, and why tire pressure changes with temperature.
Named after Joseph Louis Gay-Lussac who published this relationship in 1802, this law is the third of the foundational gas laws. It is particularly relevant for rigid containers where volume cannot change, such as sealed metal tanks, pressure vessels, and automotive tires.
Gay-Lussac's law states that at constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature:
$$\frac{P_1}{T_1} = \frac{P_2}{T_2} = k \text{ (constant)}$$
Solving for the unknown:
$$P_2 = P_1 \times \frac{T_2}{T_1} \qquad T_2 = T_1 \times \frac{P_2}{P_1}$$
The constant \(k = P/T = nR/V\) depends on the amount of gas and the volume. The physical explanation from kinetic theory is straightforward: at higher temperatures, gas molecules move faster and strike the container walls more forcefully and more frequently. Since the volume (wall area) is fixed, the pressure (force per area) increases in direct proportion to the absolute temperature.
The result gives the final pressure or temperature after the change. The P/T constant represents the proportionality factor for this specific gas sample in this container. The percentage change indicates the relative increase or decrease. Since P and T are directly proportional, a 50% increase in absolute temperature causes a 50% increase in pressure. This law is critical for safety in pressure vessel design.
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Heating a sealed container from 300 K to 450 K (a 50% temperature increase) raises the pressure by 50%, from 1 atm to 1.5 atm. This demonstrates the direct proportionality of Gay-Lussac's law.
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An aerosol can initially at 3 atm and 300 K, if heated to 900 K in a fire, would reach 9 atm — tripling the pressure. This exceeds the burst pressure of most cans, causing a dangerous explosion. Never expose pressurized containers to fire.
Gay-Lussac's law states that at constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature: P₁/T₁ = P₂/T₂. When the absolute temperature doubles, the pressure doubles. It was published by Joseph Louis Gay-Lussac in 1802.
A pressure cooker has a fixed volume and sealed lid. As the water inside is heated, the temperature rises above 100°C because the sealed container allows pressure to build. By Gay-Lussac's law, the pressure increases with temperature. The elevated pressure raises the boiling point of water to about 120°C, cooking food faster.
Aerosol cans are pressurized at room temperature. If heated (fire, direct sunlight in a car), the temperature increases and, by Gay-Lussac's law, so does the pressure. If the pressure exceeds the can's burst strength, it explodes. Most cans are rated to about 50-55°C; beyond this, rupture is possible.
Tires approximate a constant-volume container. By Gay-Lussac's law, tire pressure increases with temperature. A general rule: pressure changes by about 1 psi for every 5.5°C (10°F) temperature change. This is why tire pressure should be checked when tires are cold.
Like all gas laws, Gay-Lussac's law uses absolute temperature (Kelvin) because pressure is proportional to the average kinetic energy of molecules, which is measured from absolute zero. Using Celsius would give incorrect ratios: 20°C to 40°C is NOT a pressure doubling (it's 293 K to 313 K, only a 7% increase).
According to Gay-Lussac's law, pressure would be zero at absolute zero (0 K). This is consistent with the kinetic theory: at absolute zero, molecular motion ceases and molecules exert no force on container walls. In practice, all gases liquefy or solidify before reaching 0 K.
Gay-Lussac's law is a special case of PV=nRT. When V and n are constant, P = (nR/V)T, confirming P is directly proportional to T. The constant k = nR/V = P/T relates the specific gas amount and container volume to the pressure-temperature relationship.
Gay-Lussac's law: P₁/T₁ = P₂/T₂ (constant volume, pressure changes with temperature). Charles's law: V₁/T₁ = V₂/T₂ (constant pressure, volume changes with temperature). Both show direct proportionality with temperature but for different properties.
Yes, the constant-volume gas thermometer is based on Gay-Lussac's law. A fixed volume of gas measures temperature through pressure changes. By extrapolating P-T data to zero pressure, scientists determined absolute zero to be -273.15°C, establishing the Kelvin scale.
Pressure vessel codes (ASME Boiler and Pressure Vessel Code) require calculating maximum pressures based on temperature extremes using Gay-Lussac's law. Gas cylinders, propane tanks, and industrial storage vessels must be rated for the highest temperature they might encounter.
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