Final temperature of mixture calculator
Find the final temperature two bodies share: 100 g of water at 20 °C and 50 g of metal at 80 °C settle just a few degrees above 20 °C, because the water's heat capacity of 418 outweighs the metal's 45. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass of substance 1
- 100
- C1
- 4.18
- T1
- 20
- Mass of substance 2
- 50
- C2
- 0.9
- T2
- 80
- Heat capacity 1
- 418
- Heat capacity 2
- 45
- Total heat capacity
- 463
- Final temperature
- 25.8315334773
When two substances at different temperatures are brought into thermal contact and no heat escapes to the surroundings, energy flows until they share a single equilibrium temperature. That final temperature is a heat-capacity-weighted average of the two initial temperatures: mass times specific heat for each body sets how strongly each pulls the mixture. Students, lab prep tools, and calorimetry-style pipelines get a stable contract without installing a CAS.
Thermal equilibrium formula and when it applies
Write energy conservation for two bodies with constant specific heats and no phase change: heat lost by one equals heat gained by the other, or equivalently the sum of m c times the temperature change for each substance is zero. Expanding m1 c1 of Tf minus T1 plus m2 c2 of Tf minus T2 equals zero and solving for Tf yields the classic weighted average Tf equals open parenthesis m1 c1 T1 plus m2 c2 T2 close parenthesis over open parenthesis m1 c1 plus m2 c2 close parenthesis.
Use any coherent unit system: grams with joules per gram per degree Celsius, or kilograms with joules per kilogram per kelvin, as long as both substances share the same mass unit, the same specific-heat unit, and the same temperature scale. Absolute temperature in kelvin and Celsius intervals work the same way for differences; just keep T1 and T2 on one scale. The model assumes perfect insulation from the environment and that mixing or contact finishes before other heat paths matter.
Phase changes such as ice melting require latent-heat terms this product does not include; for pure sensible-heat equilibration of two substances, this formula is the classroom and lab standard.
Uses in class and in the lab
Call the free in-browser final temperature of mixture calculator for lecture demos, lab-notebook checks, and quick verification of hand calculations without installing Mathematica, spreadsheet templates, or a local physics stack. Source inputs follow the same retention rules as other KIT parse items. Keep classroom-scale numbers for grading oracles and document the unit system you chose so graders and learners stay consistent.
What you can do with it
Homework and lab equilibration problems
Students mix hot metal and cool water (or two liquids), submit masses, specific heats, and initial temperatures, and compare the computed equilibrium temperature to their hand calculation.
FAQ
What happens if total heat capacity is zero?
When m1*c1 + m2*c2 equals zero there is no defined equilibrium temperature from this formula, so the engine rejects the input and does not charge.
Which units should I use?
Any coherent system works (for example g and J/(g·°C), or kg and J/(kg·K)). Use the same mass unit, specific-heat unit, and temperature scale for both substances.
Is the final temperature of mixture calculator free?
The browser tool runs free on your device.
Does this include phase changes or latent heat?
No. This product models sensible-heat thermal equilibrium only. Melting, freezing, or boiling requires latent-heat terms and is outside this contract.
Does it account for heat lost to the air or the container?
No. It assumes the two substances are perfectly insulated from their surroundings and reach equilibrium before any other heat path matters. Heat that escapes to the air or to the container is not part of the calculation.
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/final-temperature-two-substances \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"m1":100,"c1":4.18,"t1":20,"m2":50,"c2":0.9,"t2":80}'const res = await fetch("https://api.kit.forhosting.com/chem/final-temperature-two-substances", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"m1": 100,
"c1": 4.18,
"t1": 20,
"m2": 50,
"c2": 0.9,
"t2": 80
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/final-temperature-two-substances",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"m1": 100,
"c1": 4.18,
"t1": 20,
"m2": 50,
"c2": 0.9,
"t2": 80
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/final-temperature-two-substances", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"m1":100,"c1":4.18,"t1":20,"m2":50,"c2":0.9,"t2":80}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"m1":100,"c1":4.18,"t1":20,"m2":50,"c2":0.9,"t2":80}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/final-temperature-two-substances", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"m1": 100,
"c1": 4.18,
"t1": 20,
"m2": 50,
"c2": 0.9,
"t2": 80
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.final_temperature_two_substances",
"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 capability computes that result deterministically from six numbers—m1, c1, T1, m2, c2, T2—returns structured JSON with per-body and total heat capacity, and rejects the singular case where total heat capacity is zero so clients never divide by zero in silence.
Thermal equilibrium formula and when it applies
Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Inputs, outputs, and the zero heat-capacity error
Send six required finite numbers: m1 and m2 for the two masses, c1 and c2 for specific heat capacities, and t1 and t2 for the initial temperatures. Zero mass or zero specific heat on only one side is allowed when the other side still contributes capacity; in that trivial case the equilibrium temperature equals the non-zero side. Documented aliases such as mass1, specific_heat1, T1, temp2, and s2 are accepted so homework forms and lab scripts can use familiar names. On success the response echoes the rounded inputs, heat_capacity_1 equal to m1 times c1, heat_capacity_2 equal to m2 times c2, total_heat_capacity as their sum, and final_temperature together with the synonym equilibrium_temperature for clients that prefer that label. The formula string and method thermal_equilibrium_two_substances let downstream code assert which model ran without sniffing shapes. If total heat capacity m1 c1 plus m2 c2 is zero, the request fails with invalid_input and a message that names zero total heat capacity—division by zero is undefined and is never charged after the engine rejects the body. Missing fields, non-finite values, and out-of-range magnitudes also fail with invalid_input.
API usage, pricing, classroom and lab workflows
Use the prepaid API when a tutoring platform, LMS auto-grader, calorimetry helper, process-engineering sandbox, or science curriculum generator needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with the single-body specific heat calculator when you need Q equals m c delta T for one substance alone, or with gas-law final-temperature tools when the intent is Charles or Gay-Lussac rather than condensed-matter contact. Authors shipping SDKs can map final_temperature and total_heat_capacity directly into UI tables that show each body mass, specific heat, initial temperature, and the shared equilibrium result—the same layout students see when they set heat lost equal to heat gained on paper.
Integration use cases
Tutoring and auto-graded drills
Lesson builders generate two-body calorimetry drills with structured JSON for flashcards and auto-graders without embedding a full physics CAS.
Process and teaching pipelines
Scripts that estimate the contact temperature of two process streams with known heat capacities call a stable prepaid endpoint instead of reimplementing the weighted average in every language.
Technical questions
How do I calculate the final temperature of a mixture of two substances?
Send JSON with m1, c1, t1, m2, c2, and t2. The response includes final_temperature equal to (m1 c1 T1 + m2 c2 T2) / (m1 c1 + m2 c2), plus heat capacities for each body.