202,650
370.950027
Pa/K
370.950027
Pa/K
2
2
1.00%
1.00%
202,650
370.950027
Pa/K
370.950027
Pa/K
2
2
1.00%
1.00%
The Gay-Lussac's Law Calculator determines how gas pressure changes with temperature when volume is held constant: P₁/T₁ = P₂/T₂. Joseph Louis Gay-Lussac demonstrated in 1808 that the pressure exerted by a confined gas rises linearly with absolute temperature.
This law is critical for understanding pressure cookers, aerosol cans in heat, tire pressure changes with temperature, and the safety of pressurized vessels. Any sealed container of gas follows this relationship — heating it increases pressure, and cooling it decreases pressure.
Gay-Lussac's Law (also called the Pressure-Temperature Law or Amontons's Law) is:
$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$
Or equivalently:
$$P = kT \quad (\text{constant at fixed } n, V)$$
where k = nR/V from the ideal gas law. Rearranging:
$$P_2 = P_1 \times \frac{T_2}{T_1}, \quad T_2 = T_1 \times \frac{P_2}{P_1}$$
Like Charles's Law, the graph of P versus T is a straight line through the origin when temperature is in Kelvin. The slope depends on the amount of gas and the container volume.
At the molecular level, increasing temperature makes gas molecules move faster and collide with the container walls more frequently and forcefully, producing higher pressure. Since the volume is fixed, the gas cannot expand to relieve this pressure — so it builds up proportionally.
The pressure change percentage tells you how much the pressure has increased or decreased, which is vital for safety calculations in engineering applications involving pressurized containers.
A positive pressure change means heating increased the pressure; negative means cooling reduced it. The P/T ratios should be equal. If the calculated pressure exceeds the burst rating of a container, the vessel may fail — always include a safety margin. Remember: temperatures must be in Kelvin.
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A tire inflated to 220 kPa at 20 °C reaches about 250 kPa at 60 °C — a 13.6% increase. This is why tire pressures are checked when tires are cold.
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An aerosol can at 300 kPa (20 °C) would reach 900 kPa at about 606 °C (879 K). Cans typically burst well before this — never expose aerosols to open flame.
Gay-Lussac's Law states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. Heating a confined gas increases its pressure proportionally.
Cold temperatures reduce the kinetic energy of air molecules inside the tire. By Gay-Lussac's Law, lower temperature means lower pressure. A typical tire loses about 1 psi for every 5.5 °C (10 °F) drop in temperature.
Yes. Guillaume Amontons discovered the pressure-temperature relationship in 1702, before Gay-Lussac's more precise measurements. Both names refer to the same law: P/T = constant at fixed volume and amount.
The fixed-volume can traps gas. As temperature rises, pressure increases according to Gay-Lussac's Law. When pressure exceeds the can's structural limit (typically 1000–1500 kPa), the can ruptures explosively.
Both the volume and the amount of gas (moles) must remain constant. The container must be rigid (no expansion) and sealed (no gas escapes). If volume changes, use the combined gas law.
A pressure cooker is a sealed, rigid vessel. Heating the water inside produces steam, and continued heating raises the temperature and pressure (Gay-Lussac's Law). Higher pressure raises the boiling point of water, allowing cooking at temperatures above 100 °C.
Roboculator Team
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