Specific Heat & Heat Energy Calculator

About the Specific Heat & Heat Energy Calculator

The heat needed to warm something is q = m c ΔT: mass times specific heat times the temperature change. This calculator solves that formula for any one unknown — the heat, the mass, the specific heat or the temperature — in joules, calories, kilocalories, Btu or kilowatt-hours, with temperatures in °C, K or °F, and gives the time a heater of a given power would take. A table of about thirty sourced specific heats (water, ice, steam, metals, glass, wood, liquids and gases) fills in c for you.

Two more modes go beyond the simple formula. Heating curve adds the latent heat of melting and boiling, so it can take ice at −20 °C all the way to steam at 120 °C stage by stage, with the classic temperature–heat graph. Mixing finds the final temperature when substances at different temperatures meet in a calorimeter — including ice that melts, or steam that condenses — or works backwards from a measured final temperature to an unknown specific heat, a starting temperature or the heat released by a reaction.

Common uses

• Chemistry and physics homework on specific heat, latent heat and calorimetry, with every substitution shown.
• Lab work: finding the specific heat of an unknown metal from a calorimetry experiment.
• Kitchen and home: the energy and time to heat water in a kettle, geyser or pot.
• Estimating the heat to melt ice or raise steam for a process.
• Checking coffee-cup and bomb-calorimeter results for reaction heats.

The formulas

• Temperature change: q = m c ΔT with ΔT = T_final − T_initial; a temperature fall makes q negative (heat given out). A change of 1 K equals 1 °C; 1 °F is 5/9 K.
• Phase change: q = m L, with L_f (fusion) for melting or freezing and L_v (vaporisation) for boiling or condensing; the temperature stays put while it happens.
• Mixing: with no heat lost, Σ m c (T_final − T_initial) = 0, so without phase changes T_final = Σ m c T_initial ÷ Σ m c. A calorimeter of heat capacity C adds C (T_final − T_cal). Ice, water and steam are handled through their total energy (enthalpy), so the answer can be “0 °C with some ice left”.
• Heater time: t = q ÷ P, ignoring heat lost to the surroundings and the heater itself — real kettles take longer.

Water’s heating curve

At normal pressure, heating 1 kg of ice from −20 °C to steam at 120 °C takes (OpenStax University Physics Vol. 2, Tables 1.3 and 1.4):

• warm the ice: 1 kg × 2,090 J/(kg·K) × 20 K = 41.8 kJ
• melt it at 0 °C: 1 kg × 334 kJ/kg = 334 kJ
• warm the water: 1 kg × 4,186 J/(kg·K) × 100 K = 418.6 kJ
• boil it at 100 °C: 1 kg × 2,256 kJ/kg = 2,256 kJ
• warm the steam: 1 kg × 2,020 J/(kg·K) × 20 K = 40.4 kJ

The total is 3.09 MJ, and 83.8 % of it goes into melting and boiling. These are textbook constants: the specific heat of water actually drifts between about 4.18 and 4.22 kJ/(kg·K) from 0 to 100 °C (IAPWS-IF97), and other references give slightly different latent heats, so the property values can be edited.

Where the specific heats come from

• OpenStax Chemistry 2e, Table 5.1 — “Specific Heats of Common Substances at 25 °C and 1 bar”: helium, water, ethanol, ice (at −10 °C), water vapour, nitrogen, air, oxygen, aluminium, carbon dioxide, argon, iron, copper, lead, gold and silicon.
• OpenStax University Physics Vol. 2, Table 1.3 — “Specific Heats of Various Substances”: water at 15 °C, ice averaged over −50 °C to 0 °C, steam at 100 °C (at constant pressure), iron or steel, silver, glass, concrete or granite, wood, the human body, benzene, glycerin, mercury and ammonia.

For gases the values are at constant pressure, which is what applies when a gas is heated in the open. Specific heats change with temperature, so treat them as averages near the stated conditions.

Sources

• OpenStax, University Physics Volume 2 (CC BY 4.0): §1.4 Heat Transfer, Specific Heat, and Calorimetry (Eq. 1.5, Table 1.3, Examples 1.5 and 1.7) and §1.5 Phase Changes (Table 1.4, the −20 °C ice heating curve, Example 1.9).
• OpenStax, Chemistry 2e (CC BY 4.0): §5.1 Energy Basics (Table 5.1, Examples 5.1–5.2) and §5.2 Calorimetry (Examples 5.3–5.7).
• IAPWS, Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97), for the temperature dependence of water’s specific heat.
• NIST, SP 811 Appendix B.8: calorie (4.184 J), Btu (IT) and the Btu/(lb·°F) = 4.1868 kJ/(kg·K) relation.

Limitations

• Specific heats are treated as constant over the temperature range; for wide ranges or high accuracy, use temperature-dependent data.
• Latent heats and transition temperatures are for normal atmospheric pressure (1 atm); water boils at lower temperatures at altitude.
• Mixing assumes a perfectly insulated system: no heat to or from the surroundings, no evaporation, no chemical reaction (except in the reaction-heat solve).
• Only water, ice and steam change phase in the mixing mode; other substances keep their specific heat (a warning appears if they would cross a melting or boiling point that is known).
• Heater times are minimums: real appliances lose heat and take longer.

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