Gay Lussacs Law Calculator - Pressure and Temperature at Constant Volume

Gay-Lussac's Law calculator is a chemistry and physics tool that solves the constant-volume relation P1 over T1 equals P2 over T2 for any one of the four variables once the other three are known. Pick the unknown, type the three known values into the form, and the calculator returns the missing pressure or temperature in the unit you started with, after converting Celsius or Fahrenheit to Kelvin internally.

• • Chemistry Homework and AP Problems: Students working rigid-container problems get the unknown pressure or temperature in the same unit the rest of the problem uses.
• • Aerosol Can Safety Checks: Lab safety officers estimate how much pressure rises in a sealed can on a hot day, a direct constant-volume problem.
• • Rigid Tank and Reactor Sizing: Process engineers size relief valves by computing the new pressure after a known temperature change at fixed volume.

This Gay-Lussac's Law pressure-temperature relation is one of three special-case gas laws taught alongside Boyle's Law and Charles's Law. It applies when the container does not change shape and the amount of gas does not change, so only pressure and temperature are free to vary. Joseph Louis Gay-Lussac published it in 1802, and it is also called Amontons's law.

When the problem crosses into Boyle's Law or Charles's Law and the volume is no longer fixed, Gas Laws Calculator keeps the same units and lets the student solve all three special gas laws in one place.

The calculator applies the constant-volume pressure-temperature ratio. Temperatures are converted to Kelvin before the ratio, and pressures are kept in the unit you selected.

• P1: Initial pressure in the rigid container. Same unit as P2.
• T1: Initial absolute temperature, converted to Kelvin.
• P2: Final pressure after the temperature change. Same unit as P1.
• T2: Final absolute temperature, converted to Kelvin.
• Pressure Unit: Applied to both P1 and P2. Supported: atm, kPa, bar, psi, mmHg.
• Temperature Unit: Applied to both T1 and T2. Supported: K, C, F.

Rearranging isolates the unknown. When P2 is unknown, P2 = P1 * (T2 / T1). When T2 is unknown, T2 = T1 * (P2 / P1). The same rearrangements work backward for P1 or T1. The calculator checks each input for validity: pressures must be non-negative, and temperatures must convert to a positive Kelvin value.

According to NIST SI Units, 0 degrees Celsius equals exactly 273.15 K, the offset used in every gas-law temperature conversion.

According to Wikipedia, Gay-Lussac's law, the pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature.

When the moles of gas are not constant because the container is opened or a reaction changes the amount of gas, Ideal Gas Calculator covers the full PV equals nRT form.

Four small concepts explain why the relation is limited to constant volume and constant amount of gas, and why the temperature must be in Kelvin.

Because this is one of three special cases, the calculator is intentionally narrow. Once volume or moles change, the combined gas law or the ideal gas law is the right tool.

When the homework asks for the density of the gas in the rigid container before and after the temperature change, Gas Density Calculator extends the same inputs to mass per unit volume so the two states can be compared.

Six short steps take you from a written chemistry problem to a clean answer that lines up with the textbook solution.

1. 1 Identify the Unknown: Read the problem and pick which one of P1, T1, P2, T2 is missing. That field becomes the solve-for choice.
2. 2 Pick the Pressure Unit: Choose the pressure unit the problem uses. Both P1 and P2 share the same unit selector.
3. 3 Pick the Temperature Unit: Choose the temperature unit the problem uses. The calculator converts Celsius or Fahrenheit to Kelvin automatically.
4. 4 Enter the Three Known Values: Type the three known pressures or temperatures into the form. The initial row holds P1 and T1 and the final row holds P2 and T2.
5. 5 Choose Solve For: Use the solve-for dropdown at the top of the form to mark which value the calculator should return. The other three inputs stay as you typed them.
6. 6 Read the Result and the Ratios: Read the solved pressure or temperature at the top of the results panel. The pressure and temperature ratios beneath it should match, because P2 over P1 equals T2 over T1 in Kelvin. Matching ratios are the sanity check.

A rigid metal can holds nitrogen at 1.0 atm and 300 K in the lab. The can is moved to a storage room where the temperature reaches 450 K. To find the new pressure, pick P2 as the unknown, keep atm and K, type 1.0 for P1, 300 for T1, and 450 for T2. The result is 1.5 atm, a 50 percent rise that matches the textbook example.

When the rigid container is part of an outdoor experiment and the student needs a quick estimate of the ambient temperature at the test site, Altitude Temperature Calculator gives the same Kelvin-converted reading the gas law expects.

A small dedicated constant-volume calculator saves time on chemistry homework, prevents unit-conversion mistakes, and produces a result that lines up with how the relation is taught.

• • Solves Any One of the Four Variables: Returns whichever of P1, T1, P2, T2 is missing, so the same form handles every constant-volume problem.
• • Keeps the Pressure Unit: Accepts atm, kPa, bar, psi, or mmHg and returns the answer in the same unit.
• • Converts Celsius and Fahrenheit to Kelvin: Applies the 273.15 offset and the Fahrenheit conversion before the ratio, removing the most common mistake: using Celsius in the denominator.
• • Shows the Ratios for Sanity Checking: Returns the pressure and temperature ratios side by side. When they match, the result is correct.
• • Built for Closed Rigid Containers: The helper text and worked examples remind the user that the formula only applies at constant volume and constant moles.

The biggest practical benefit is removing the Celsius-in-the-denominator mistake. Students type 27 and 127 into a gas-law formula, get a wrong answer, and assume the formula is wrong. The calculator converts the values to 300.15 K and 400.15 K before applying the ratio, so the answer matches the textbook every time the inputs are valid.

Five physical and process factors set the practical bounds of the constant-volume pressure-temperature ratio.

• • The relation applies only at constant volume and constant moles. The calculator surfaces this in the helper text but cannot detect whether the physical container satisfies the constraint.
• • The formula treats the gas as ideal. Above a few atmospheres or near the condensation point, real-gas deviations matter and the calculated pressure will differ from the measured value.
• • The temperature must convert to a positive Kelvin value. The calculator rejects inputs at or below -273.15 C (0 K) because the ratio is undefined there.

Real-world uses include pressure-cooker safety, aerosol-can storage, hot-air balloon envelopes, and rigid compressed-gas tanks. The formula gives a first-pass pressure estimate good enough to size a relief valve or plan a storage temperature limit, then real-gas corrections refine it as conditions approach the edge of the ideal-gas regime.

According to Khan Academy, Gay-Lussac's Law, heating a fixed amount of gas in a rigid container from 300 K to 450 K raises the gas pressure by the same factor of 450 divided by 300, which is the standard textbook example for the constant-volume pressure-temperature ratio.

When the rigid container also holds water vapor and the problem asks how the partial pressure of water inside changes with temperature, Vapor Pressure Deficit Calculator pairs the ideal-gas temperature ratio with the saturation-pressure curve so the answer includes humidity effects.