Gay-Lussac law calculator
A sealed gas at 1 atm and 273.15 K heated to 373.15 K rises to about 1.3660992129 atm. Enter the starting pressure and kelvin temperature plus one final value, and the other one is solved at constant volume. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- P1
- 1
- T1
- 273.15
- T2
- 373.15
- P2
- 1.3660992129
- Solved
- p2
- Constant
- volume
Gay-Lussac’s law states that for a fixed amount of ideal gas held at constant volume, absolute pressure is proportional to absolute temperature: the ratio P over T stays the same when the system is heated or cooled isochorically. Students checking isochoric homework, teachers building answer keys, lab technicians relating gauge readings to oven setpoints, and engineers sanity-checking sealed vessels all need the same inputs—initial pressure, initial kelvin temperature, and one final value—and a clear missing final pressure or temperature.
What Gay-Lussac’s law means and which quantities you need to send
In introductory thermodynamics and chemistry, Gay-Lussac’s law (sometimes called Amontons’ law for the pressure–temperature form) describes an isochoric process: volume and amount of gas stay fixed while pressure and absolute temperature change together. The compact statement is P1 divided by T1 equals P2 divided by T2, where temperatures are absolute kelvin (or another absolute scale) and pressures are absolute, not gauge.
Search intent clusters around phrases such as Gay-Lussac law calculator, pressure temperature constant volume, isochoric P over T, P1/T1 equals P2/T2 solver, and final pressure from temperature change at fixed volume. People want a numeric answer they can check against a worksheet, embed in a lab report, or feed into a larger pipeline—not only a reminder that the formula exists.
Keep pressure units consistent between the initial and final states; the engine does not convert atmospheres to pascals or Celsius to kelvin for you, so convert to absolute kelvin before calling.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate constant-volume P–T check while grading homework, verifying a sealed-vessel heat-up estimate, relating a tank pressure rise to an oven temperature change, or sanity-checking a simulation isochoric step. Choose units consistently—if pressures are in atmospheres or pascals on both sides and temperatures are kelvin, the solved final value stays in the same unit family. Results are fully deterministic: the same three inputs always yield the same p1, t1, p2, t2, solved flag, and the same formula and method labels.
There is no language model, no external thermodynamics service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials.
What you can do with it
Homework and isochoric gas-law drills
Students and graders confirm final pressure or temperature for fixed-volume heating and cooling problems, with clear rejection when kelvin temperatures are zero or negative.
Sealed-vessel pressure rise sketches
Quick structured estimates of how absolute pressure tracks absolute temperature when volume is held constant, without standing up a full process simulator.
FAQ
Which formula does the calculator use?
Gay-Lussac’s isochoric law: P1/T1 = P2/T2. Known T2 yields P2 = P1·T2/T1; known P2 yields T2 = T1·P2/P1. Temperatures must be absolute kelvin.
What happens if temperature is zero or negative?
Non-positive kelvin is rejected and those calls are not charged.
Is the Gay-Lussac law calculator free?
The browser tool runs free on your device.
Can I send both final pressure and final temperature?
No. Provide exactly one of p2 or t2—the unknown you want solved.
Can I enter gauge pressure or degrees Celsius?
No. The law works with absolute pressure and absolute temperature, and the calculator does not convert either one. Turn gauge readings into absolute pressure and Celsius into kelvin before you enter them.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/thermo/gay-lussac-law \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"p1":1,"t1":273.15,"p2":1.366}'const res = await fetch("https://api.kit.forhosting.com/thermo/gay-lussac-law", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"p1": 1,
"t1": 273.15,
"p2": 1.366
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/gay-lussac-law",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"p1": 1,
"t1": 273.15,
"p2": 1.366
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/gay-lussac-law", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"p1":1,"t1":273.15,"p2":1.366}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"p1":1,"t1":273.15,"p2":1.366}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/gay-lussac-law", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"p1": 1,
"t1": 273.15,
"p2": 1.366
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.gay_lussac_law",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This capacity rearranges P1/T1 equals P2/T2 deterministically, rejects non-positive kelvin with a clear invalid_input error, and returns structured JSON with both state points, which quantity was solved, the formula, and the constant-volume method label.
What Gay-Lussac’s law means and which quantities you need to send
Delivering p1, t1, p2, t2, solved, formula, method, and constant as JSON makes the result easy to paste into notes, diff in automated tests, or reuse across languages without reimplementing the rearrange-and-divide arithmetic.
How this calculator validates input and applies P1/T1 = P2/T2
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Absolute pressures must be positive as well. Providing both p2 and t2 is rejected because the system would be over-specified; providing neither is rejected because there is nothing to solve. There is no Boyle or Charles branch, no amount-of-substance term, and no unit conversion service; this is pure Gay-Lussac for the three known quantities at constant volume. Send a JSON body with required fields p1 and t1, plus exactly one of p2 or t2—the unknown final quantity you want solved. Every numeric field must be finite: missing required fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are supported: initial_pressure and P1 for p1; initial_temperature and T1 for t1; final_pressure and P2 for p2; final_temperature and T2 for t2. Absolute temperatures must be strictly positive kelvin: zero or negative t1 or t2 is always rejected as invalid_input because the ideal-gas absolute scale does not admit non-positive temperatures in this model. After validation, the engine applies P2 equals P1 times T2 over T1 when temperature is known, or T2 equals T1 times P2 over P1 when pressure is known, and rounds to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. The same pure function powers the free in-browser tool and the API path.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Wire the endpoint into gas-law drills, contest answer checkers, process-sketch tools, or preprocessing steps where you already prefer explicit domain errors—such as rejecting non-positive kelvin—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for thermo tests
Pipelines that seed unit tests or interactive science demos can call a pure P1/T1=P2/T2 oracle instead of reimplementing Gay-Lussac arithmetic in every language.
Technical questions
How do I use this Gay-Lussac law calculator?
Send JSON with p1, t1, and exactly one of p2 or t2 to thermo.gay_lussac_law. The response returns both final values, which field was solved, and formula P1/T1=P2/T2.