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Gay-Lussac's Law Calculator

Solve any of initial or final pressure and temperature for a fixed gas at constant volume, using P₁/T₁ = P₂/T₂. Pressure is directly proportional to absolute temperature — heat a sealed container, the pressure rises.

P₁/T₁ = P₂/T₂
Constant volume
Temperature in kelvin
Solve any value
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Gay-Lussac's Law — Quick answer

At constant volume, a gas's pressure is directly proportional to its absolute temperature (in kelvin).

P₁ / T₁ = P₂ / T₂ (T in kelvin)
P₂ = P₁·T₂ / T₁ · T₂ = T₁·P₂ / P₁

Worked example: 1 atm at 300 K heated to 600 K in a rigid tank. P₂ = 1 × 600 / 300 = 2 atm.

1 atm at 300 K, rigid container heated

TemperaturePressureNote
300 K (27 °C)1 atmstart
450 K1.5 atm×1.5
600 K2 atmdouble temp

Used for: aerosol cans, pressure cookers, tyres, sealed tanks.

🧪 Gay-Lussac's Law Calculator

Leave the one unknown blank. Temperatures in kelvin (°C + 273.15); both pressures share a unit.

Initial pressure P₁
Initial temp T₁
Final pressure P₂
Final temp T₂

⚠️ Temperatures must be absolute — kelvin. Convert with T(K) = °C + 273.15 (27 °C = 300 K). The container volume and the amount of gas are assumed fixed; if volume can change, use the combined gas law.

Gay-Lussac's Law — the pressure law — describes a gas trapped in a rigid container: at constant volume the pressure is directly proportional to the absolute temperature, so P₁/T₁ = P₂/T₂. Heat the gas and the molecules strike the walls harder and more often, driving the pressure up in proportion to the kelvin temperature; cool it and the pressure falls. It is why sealed cans and pressure vessels become dangerous when heated, and why tyre pressure rises on a hot day.

Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Gay-Lussac's Law as the constant-volume case of PV = nRT.

The Gay-Lussac's Law equations

Gay-Lussac's Law
P₁ / T₁ = P₂ / T₂ (T in kelvin)
Final pressure
P₂ = P₁ × T₂ / T₁
Kelvin conversion
T(K) = T(°C) + 273.15

The ratio of pressure to absolute temperature is constant for the gas while volume and amount stay fixed. To find a missing quantity, set the two ratios equal and cross-multiply. The pressure unit cancels — atm, kPa, bar or psi all work — but the temperatures must be in kelvin, since pressure is proportional to absolute temperature, measured from absolute zero.

Worked example — heating a sealed tank

Scenario: A rigid tank holds gas at 1 atm and 300 K (27 °C). It is heated to 600 K. What is the new pressure?

Final pressure
P₂ = 1 atm × 600 K / 300 K = 2 atm
Check the ratio
1 / 300 = 0.00333 = 2 / 600 ✓

Doubling the absolute temperature doubles the pressure to 2 atm — the ratio P/T holds at 0.00333 atm/K throughout. Heat the tank to only 450 K and the pressure reaches 1.5 atm (a factor of 1.5, matching 450/300). This is exactly the hazard behind aerosol-can warnings: a sealed container's pressure climbs in lockstep with absolute temperature, and a strong enough heat source can push it past the bursting point.

Frequently Asked Questions

What is Gay-Lussac's Law?

At constant volume, gas pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. Double the kelvin, double the pressure.

How do I find the new pressure?

P₂ = P₁·T₂/T₁. e.g. 1 atm × 600 K ÷ 300 K = 2 atm. New temp is T₂ = T₁·P₂/P₁.

Why kelvin?

It uses absolute temperature from absolute zero. Add 273.15 to °C; Celsius gives wrong, even negative, pressures.

Why do aerosol cans warn against heat?

A sealed can is constant volume — heating doubles the pressure as kelvin doubles, and it can burst.

How is it different from Charles's Law?

Charles holds pressure constant (V vs T); Gay-Lussac holds volume constant (P vs T). Both are proportional to kelvin.

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