What to enter
The calculator needs three numbers, all in SI units. Typical specific heats near room temperature are water 4,186, ice 2,100, aluminum 900, iron 450 and copper 385 J/(kg·K). These are rounded, so use a measured figure if you have one.
- Mass in kilograms. Divide grams by 1,000. One litre of water is about 1 kg.
- Specific heat in J/(kg·K). The default of 4186 is liquid water. If your table gives kJ/(kg·K), multiply by 1,000, or your answer will be 1,000 times too small.
- Temperature change in kelvin, which is the final temperature minus the starting temperature. A change of 1 K equals a change of 1 °C, so 20 °C to 100 °C is simply 80. For a Fahrenheit difference, multiply by 5/9 first.
The formula: Q = mcΔT
Q = m × c × ΔT, where Q is heat energy in joules, m is mass, c is specific heat and ΔT is the temperature change. Specific heat is the energy one kilogram of a material takes to warm by one kelvin. Multiplying by the mass and the number of kelvin scales that up to your case.
Worked example: boiling a full kettle
A kettle holds 2 litres of water at 20 °C. How much energy does it take to reach 100 °C? Enter Mass 2, Specific Heat 4186 and Temperature Change 80. The result is 669,760, from 2 × 4186 × 80, which is about 670 kJ.
A 2,000 W kettle delivers 2,000 joules each second, so the ideal time is 669,760 ÷ 2,000 = 335 seconds, or about 5.6 minutes. A real kettle takes longer because some heat escapes.
Swap the water for 2 kg of aluminum at 900 J/(kg·K) and the result falls to 144,000, less than a quarter of the energy for the same temperature rise.
Reading the result
The result is in joules, although the page prints only the number. Divide by 1,000 for kilojoules, by 4,184 for kilocalories, or by 3,600,000 for kilowatt-hours. So 669,760 J is about 160 kcal, or 0.186 kWh.
A positive result is heat taken in. A negative temperature change gives a negative result, which is heat given out as the material cools.
Limits
- No change of state. Melting and boiling absorb heat with no temperature rise, and this formula leaves that out. Melting ice takes about 334 kJ/kg, and boiling water away takes about 2,260 kJ/kg, on top of any warming.
- Specific heat is treated as constant. It really varies with temperature, though for liquid water only by about 1% between 0 °C and 100 °C.
- All the heat is assumed to reach the material, with none lost to the container or the air.
- For gases, the value differs depending on whether pressure or volume is held fixed, so use the one that matches your situation.