# Calorimetry Calculator - q = mcΔT, Specific Heat, Final Temperature, Ice Melting & Heating Curve

> Free calorimetry calculator: solve q = mcΔT with a specific heat table, find the final temperature of mixtures, get ΔH from coffee-cup and bomb calorimetry.

- URL: https://qilingtools.com/en/math/calorimetry
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Chemistry](https://qilingtools.com/en/tags/chemistry), [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

The heat absorbed or released when something changes temperature is q = m·c·ΔT, where c is the specific heat capacity: 4.184 J/(g·K) for water, about 2.09 for ice, 2.01 for steam, 0.897 for aluminium, 0.385 for copper and 0.449 for iron. Heating 100 g of water from 20 °C to 80 °C takes 100 × 4.184 × 60 = 25,104 J, about 25.1 kJ. The first tab solves any one of q, m, c and ΔT from the other three and includes specific heats for more than 30 common substances. The mixing tab applies energy conservation (Σq = 0) to two or more bodies and handles water's phase changes properly: 100 g of water at 80 °C mixed with 50 g at 20 °C ends at 60 °C; 50 g of ice at 0 °C dropped into 200 g of water at 25 °C melts completely, because cooling the water to 0 °C releases 20.9 kJ while melting the ice needs only 16.7 kJ, and the mixture ends near 4.0 °C. When there is not enough heat, the result is an ice–water mixture at 0 °C and the tool reports how much ice is left. The coffee-cup tab turns a temperature change into a reaction enthalpy, q_rxn = −(q_soln + q_cal), divided by moles to give ΔH of neutralisation or dissolution, with the sign convention explained. The bomb calorimeter tab calibrates the heat capacity with benzoic acid (26.43 kJ/g), then gives ΔcU of a sample per gram and per mole, works out Δn(gas) from the formula and converts to ΔcH = ΔcU + Δn(g)RT. Finally the heating-curve tab totals the heat needed to take ice, water or steam from one temperature to another, listing each warming, melting (334 J/g) and boiling (2257 J/g) stage and drawing the temperature vs heat curve; turning 10 g of ice at −10 °C into steam at 110 °C takes about 30.5 kJ.

## How to use

1. Choose a tab: q = mcΔT, mixing equilibrium, coffee-cup, bomb calorimeter or heating curve, or load an example
2. Pick a substance or type a specific heat, then enter masses, temperatures and solution or sample data
3. Read the heat, final temperature, ΔH or heat of combustion and the heating curve, with every step of the working

## Features

- Solve any of q, m, c or ΔT in q = mcΔT, heat in J or kJ
- Specific heat table of 30+ substances: water, ice, steam, metals, glass, ethanol, rock, air and more
- Final temperature of two or more mixed bodies, with partial or complete melting of ice and condensing steam
- Heat gained or lost by each body and its final state (ice, water, ice–water mixture)
- Coffee-cup calorimetry: solution mass or volume × density, calorimeter constant, ΔH with sign convention
- Moles of reactant from n, concentration × volume, or mass plus formula
- Bomb calorimetry: benzoic acid calibration, ΔcU per gram and per mole, automatic Δn(gas), conversion to ΔcH
- Heating or cooling curve of water: stage-by-stage heat table and temperature vs heat plot

## FAQ

### How do I tell whether ice will melt completely in water?

Compare the heat the warm water can release cooling to 0 °C (still liquid) with the heat needed to warm the ice to 0 °C and melt all of it. 200 g of water at 25 °C can release 200 × 4.184 × 25 ≈ 20.9 kJ, while melting 50 g of ice at 0 °C needs 50 × 334 = 16.7 kJ. Since more heat is available, all the ice melts and the remaining 4.2 kJ warms the 250 g of water by about 4.0 °C. If less heat is available, the mixture stays at 0 °C with some ice left.

### What is the sign convention in coffee-cup calorimetry?

The solution and calorimeter absorb q = mcΔT (positive when they warm), and the reaction releases the same heat with the opposite sign: q_rxn = −(q_soln + q_cal). At constant pressure q_rxn equals ΔH. A temperature rise means an exothermic reaction with negative ΔH, such as neutralisation at about −56 kJ/mol; a temperature drop means an endothermic process, such as dissolving ammonium nitrate at about +25.7 kJ/mol.

### Does a bomb calorimeter measure ΔU or ΔH?

A bomb calorimeter has a fixed volume, so it measures the internal energy of combustion, ΔcU. Convert it with ΔcH = ΔcU + Δn(g)·RT, where Δn(g) is moles of gaseous products minus gaseous reactants in the combustion equation (water as liquid). For naphthalene, C₁₀H₈ + 12 O₂ → 10 CO₂ + 4 H₂O(l), Δn(g) = −2, so ΔcH is about 5 kJ/mol more negative than ΔcU.

### How much heat turns ice at −10 °C into steam at 110 °C?

Add five stages: warm the ice (m × 2.09 × 10), melt it (m × 334), warm the water from 0 to 100 °C (m × 4.184 × 100), boil it (m × 2257) and warm the steam (m × 2.01 × 10). For 10 g that is 209 J, 3340 J, 4184 J, 22,570 J and 201 J, about 30.5 kJ in total. Boiling alone takes over 70%, which is why the 100 °C plateau is the longest part of the heating curve.

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