How to use the heating curve energy calculator
- Enter the mass of water in grams.
- Enter the starting temperature and the final temperature in Celsius.
- Review the constants: the specific heats of ice, water and steam, the heats of fusion and vaporization, and the melting and boiling points. They are examples you can change.
- Read the total heat and a table with the heat for each stage, as joules and as a share of the total.
Formula
Within a phase: Q = mass x specific heat x temperature change
Melting: Q = mass x heat of fusion, with the temperature fixed at the melting point
Boiling: Q = mass x heat of vaporization, with the temperature fixed at the boiling point
Total heat = the sum of the stages from the start to the final temperature
The temperature of water does not change while it melts or boils, so the heat of those stages goes into the change of state. Those stages usually dominate the total.
100 g of ice at -10 C heated to steam at 110 C
Using 2.09 J/(g C) for ice, 4.186 for water, 2.01 for steam, 334 J/g for fusion and 2256 J/g for vaporization, the stages are 2090 J to warm the ice, 33400 J to melt it, 41860 J to warm the water to 100 C, 225600 J to boil it and 2010 J to warm the steam. The total is 304960 J, or 304.96 kJ.
Boiling alone takes 74 percent of the energy. Heating 250 g of water from 20 C to boiling takes 83720 J, and 50 g of ice at -5 C taken to water at 5 C takes 18269 J.
Reading the stages
The table lists only the stages the water actually passes through. Starting at 20 C gives just one stage up to the boiling point, and ending below 0 C gives only a warming of the ice. A start exactly at the melting point counts as ice that still has to melt.
To turn the heat into a running cost, see the water heater running cost calculator. To work with the amount of substance, use the moles to grams calculator.
Other substances and pressures
The constants on the page are examples for water at ordinary pressure. For another substance, enter its own specific heats, heats of change and transition temperatures. At a different pressure the boiling point moves, so enter the new boiling point. Specific heat also varies a little with temperature, which the page treats as constant.
If you treat the steam as a gas, the ideal gas law calculator relates its pressure, volume and temperature.
Assumptions and limits
- Specific heats are constant within each phase, and heats of change are those at the transition temperature.
- No heat is lost to the surroundings or the container.
- The final temperature must be above the starting temperature.
- Values are examples for water at ordinary pressure. Check them for your case.
Frequently asked questions
What is a heating curve?
It is a graph of temperature against heat added. It rises in slopes while a phase warms and is flat while the substance melts or boils.
Why does boiling take so much heat?
Breaking the bonds between molecules in the liquid takes a lot of energy. For water the heat of vaporization is about 540 times the heat to warm one gram by 1 degree.
Can I use other substances?
Yes. Replace the specific heats, heats of fusion and vaporization and the transition temperatures with values for your substance.
What are the calorie figures?
The page also gives the heat in calories using 4.184 joules per calorie, for those who work in that unit.