Work of gas expansion calculator
A gas expanding by 2 L against a constant 1.5 atm does −3 L·atm of work under the chemistry sign convention. Enter the external pressure and the volume change to get the signed work, its size and whether it was an expansion or a compression. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- P ext
- 1.5
- Delta V
- 2
- Work
- -3
- Work magnitude
- 3
- Process
- expansion
- Sign convention
- work_on_system
This work of gas expansion calculator finds the mechanical work for irreversible expansion or compression against a constant external pressure. You supply the opposing external pressure and the volume change delta V equals final volume minus initial volume; the engine applies the closed-form chemistry convention W equals negative P external times delta V. Positive delta V means expansion and yields negative work on the system; negative delta V means compression and yields positive work on the system; zero volume change yields zero work. Zero external pressure models free expansion into vacuum and always returns zero work. Negative external pressure is rejected rather than inventing an unphysical result. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Work against a constant outside pressure
In introductory chemical thermodynamics, many textbook problems ask for the work when a gas expands or is compressed against a piston held at a fixed external pressure rather than along a reversible path. That process is irreversible in the thermodynamic sense because the system pressure is not always equal to the opposing pressure, but the mechanical work integral still collapses to a simple product: the constant external pressure times the volume change, with a sign that depends on whether you count work done by the system or on the system.
This calculator uses the chemistry convention that work done on the system is positive, so W equals negative P external times delta V. Expansion increases volume, so delta V is positive and W is negative; the system does work on the surroundings. Compression decreases volume, so delta V is negative and W is positive; the surroundings do work on the system.
Units of work are whatever product of pressure and volume units you chose: litre-atmospheres, joules, or any other consistent pair. There is no automatic conversion between atmospheres and pascals, no logarithmic reversible path, and no ideal-gas assumption beyond the mechanical formula itself.
Where constant-pressure work fits in study, lab work, and software
Students meet irreversible expansion work when a textbook moves from the first law to piston problems, when a homework set gives a fixed external pressure in atmospheres and a volume change in litres and expects work in litre-atmospheres, or when a contest problem asks whether expansion work is positive or negative under a stated sign convention. Teachers can pre-generate answer keys for modest pressure and volume values without trusting opaque calculator apps that silently switch between work-by and work-on conventions or drop the minus sign.
Lab instructors use the same closed form when a protocol records piston displacement under a known external load and students must report mechanical work before comparing heat and delta U. Developers call the same contract from scripts to seed deterministic test vectors for thermodynamics tutors, to normalize user-entered pressure and volume deltas before a notebook export, or to satisfy programming-challenge statements that demand W equals negative P delta V rather than a reversible logarithmic path.
What you can do with it
Homework and first-law drills
Compute irreversible expansion or compression work from P_ext and ΔV for textbook piston problems and first-law energy balances.
Lab and teaching software
Normalize student-entered external pressure and volume change into signed work with expansion/compression labels for demos and lab notebooks.
FAQ
What does the work of gas expansion calculator cost?
It is free in your browser on this page.
What formula does this tool use?
W = −P_ext · ΔV under the chemistry sign convention (work done on the system). ΔV is V_final − V_initial; units of W are pressure×volume.
What happens if external pressure is negative?
External pressure must be zero or positive for this constant-P_ext work formula.
Does this compute reversible isothermal work?
No. It only evaluates irreversible work against constant external pressure. Reversible ideal-gas work uses −nRT ln(V₂/V₁) and is a different tool.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
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/chem/work-gas-expansion \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"P_ext":1.5,"delta_V":2}'const res = await fetch("https://api.kit.forhosting.com/chem/work-gas-expansion", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"P_ext": 1.5,
"delta_V": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/work-gas-expansion",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"P_ext": 1.5,
"delta_V": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/work-gas-expansion", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"P_ext":1.5,"delta_V":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"P_ext":1.5,"delta_V":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/work-gas-expansion", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"P_ext": 1.5,
"delta_V": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.work_gas_expansion",
"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.
Limits
max_abs_value | 1000000000000000 |
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
What irreversible expansion work means and what the response contains
The response returns the validated external pressure and delta V, the signed work, the absolute work magnitude, a process label expansion compression or isochoric, a sign_convention tag work_on_system, the method tag irreversible_constant_P_ext, the precision used, and a short formula string. The engine either multiplies the two finite scalars inside the supported numeric range or rejects the input with invalid_input. Rejected cases include missing required fields, non-finite values, magnitudes above the documented ceiling, and any negative external pressure so a bad worksheet cell does not become a silent unphysical work value.
How P_ext and delta_V are read and how results stay reproducible
External pressure must be finite and non-negative; zero is allowed and models free expansion into vacuum, which contributes no mechanical work under this formula. Volume change may be positive, negative, or zero; only the signed product with pressure determines the work. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a mistyped cell does not become a wrong sign on W. The preferred fields are P_ext for the constant external pressure and delta_V for the volume change, but aliases P, pressure, external_pressure, and p_ext for pressure, and dV, volume_change, deltaV, Delta_V, and d_v for the volume change are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for every numeric output field, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the constant-pressure work product yourself.
Where constant-pressure work fits in study, lab work, and software
Product and education tools use the endpoint when a learner types external pressure and volume change and the UI must show signed work with process labels for expansion and compression. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with ideal-gas or combined-gas helpers when you need related state checks, and with other science endpoints when you are building a small lab of free, deterministic chemistry calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible W = −P_ext·ΔV values for unit tests, chemistry tutors, and CI assertions on signed work.