Heat Calculator: Quantity of Heat with Steps and Heating Curve

Online tool for calculating the quantity of heat in heating and cooling, melting and freezing, boiling and condensation. It plots a heating curve — temperature versus time with labeled segments — and writes out the solution in the “Given — SI — Solution — Answer” format.

How to solve a quantity of heat problem

3 steps
1

Paste the problem text into the field, or choose the substance, mass and temperatures by hand.

2

Check that the tool understood the problem correctly and, if needed, choose what to find.

3

Copy the solution and the graph into your notebook or save them as a PDF.

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Solve a heat problem and draw the heating curve

Graph

Move along the graph — the temperature, the stage and the heat absorbed at that point will appear here.

Table of graph points
Check your answer

Enter the answer you got — the tool will tell you whether it is correct and, if not, where the mistake most likely is.

Example problems

Melting and freezing

Boiling and condensation

Fuel, heaters, efficiency

Heat balance (calorimetry)

Value tables

Values in gray are not in the table of the selected set: they come from a reference handbook.

Table values
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Features

Paste a problem from your textbook — the tool finds the substance, mass, temperatures and the unknown, and shows how it understood them.
Any path through the phases: ice at −20 °C → water → steam at 120 °C and back, with Q = mcΔT, Q = mLf and Q = mLv for each segment.
Temperature versus time or versus heat: letters A, B, C at the corners, melting and boiling plateaus, and a notebook mode with a grid scale.
Reverse problems: what temperature it reaches, how much ice melts, what mass can be heated, how much time and fuel it takes, what the efficiency is.
Heat balance for 2–5 objects and a calorimeter cup — including the case when not all the ice melts and the mixture settles at 0 °C.
Values from the table you choose: a precise reference, a US chemistry course, or Russian textbook and exam tables — so the answer matches your book.

Why the answers match your textbook

The answer depends on which table values are used: US chemistry courses give 334 J/g for the heat of fusion of ice, physics references 3.33·10⁵ J/kg, and Russian textbooks 3.4·10⁵ J/kg; the specific heat of copper is 385, 400 or 380 J/(kg·°C) depending on the source. So the values come from the table you select, and if a value is missing there, the solution says so. Reverse problems are solved the textbook way: first the tool checks whether there is enough heat to reach the melting point, then whether there is enough to melt all of the substance, and only then calculates how much melts.

Frequently asked questions

Why does the temperature stay the same during melting, even though heat is being added?

The energy does not speed up the particles — it breaks down the crystal lattice: particles leave their fixed positions and the substance becomes a liquid. Until the last crystal has melted, the temperature stays at the melting point, so the graph shows a horizontal segment. Its length is proportional to mLf: the larger the latent heat of fusion and the mass, the longer the plateau.

How do I draw the graph if the problem does not give the heater power?

Assume the heater is the same at every stage. Then time is proportional to the heat absorbed, and the length of each segment of the graph is proportional to the Q of that segment. The time scale is arbitrary, while the temperatures are labeled exactly. If the substance starts at its melting point, the graph begins with the horizontal segment right away. In notebook mode, the tool picks a grid scale so that the points land on grid lines.

Why is my answer a few percent off from the answer key?

It is almost always the table values. The specific heat of water is 4186 J/(kg·°C) in most physics books (4.184 J/(g·°C) in chemistry) and 4200 in others; the latent heat of fusion of ice is 333 or 334 kJ/kg (340 kJ/kg in Russian textbooks); the latent heat of vaporization is 2260 or 2300 kJ/kg. Choose the table of your textbook in the settings or enter the numbers from the problem. Checking your own answer tells you which table it is correct for.

Ice was dropped into warm water — why is the result 0 °C with some ice left?

Warm water cooling down to 0 °C can give off only a limited amount of heat. If that heat is less than what it takes to warm the ice to 0 °C and melt all of it, only part of the ice melts, and the glass settles at 0 °C: at this temperature ice and water are in equilibrium. The mass of melted ice equals the leftover heat divided by Lf.

Why are the specific heats of ice and water different if it is the same substance?

Specific heat capacity depends not only on the substance but also on its state: ice has about 2100 J/(kg·°C), liquid water 4186, and steam about 2010. That is why heating ice and heating water are separate stages with separate formulas, and on the graph they have different slopes: at the same power, ice warms up about twice as fast as water.

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