Heat Transfer Calculator (Q = mcΔT and Mixing Temperature)
Pick a material from the list of specific heats (or enter your own), the mass and the temperatures. You get the heat in joules, kilocalories and kilowatt-hours, or the equilibrium temperature of a mixture.
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Formula
- Heat to change a temperature:
Q = m × c × ΔT(m in kg, c in J/(kg·K), ΔT in K or °C; a change of 1 °F is 5/9 K). - Mixing two substances:
Tf = (m1·c1·T1 + m2·c2·T2) ÷ (m1·c1 + m2·c2). - Conversions:
1 kcal = 4184 J,1 kWh = 3 600 000 J,1 lb = 0.45359237 kg.
Assumptions: no phase change (no melting or boiling), constant specific heat, no heat lost to the surroundings or container. A negative Q means the substance gives heat out.
Worked example
Warming 2 kg of water from 20 °C to 80 °C: Q = 2 × 4184 × 60 = 502 080 J = 120 kcal = 0.1395 kWh.
Dropping 0.2 kg of copper at 100 °C into 0.5 kg of water at 20 °C: Tf = (0.2×385×100 + 0.5×4184×20) ÷ (0.2×385 + 0.5×4184) = 49 540 ÷ 2 169 = 22.84 °C, and the copper gives up 0.2 × 385 × (100 − 22.84) = 5 941 J.
Frequently asked questions
What is the heat transfer formula Q = mcΔT?
Q = m × c × ΔT, where m is the mass in kg, c the specific heat in J/(kg·K) and ΔT the temperature change. Warming 2 kg of water from 20 °C to 80 °C takes 2 × 4184 × 60 = 502,080 J, which is 120 kcal or 0.139 kWh.
How is the final temperature of a mixture found?
Heat lost by the hot substance equals heat gained by the cold one, so Tf = (m1·c1·T1 + m2·c2·T2) ÷ (m1·c1 + m2·c2). A 0.2 kg copper block at 100 °C dropped into 0.5 kg of water at 20 °C settles at (7,700 + 41,840) ÷ (77 + 2,092) = 22.84 °C.
Why does water change temperature so slowly?
Water has one of the highest specific heats of common materials, 4184 J/(kg·K), about 11 times that of copper (385). It takes a lot of energy to warm and releases a lot when it cools, which is why it is used in heating systems and moderates climate.
Does the calculator include melting or boiling?
No. It assumes the material stays in one phase and the specific heat is constant over the range. Melting ice or boiling water absorbs extra latent heat that is not included, so results near 0 °C or 100 °C for water are only valid if no phase change happens. Mixing also assumes no heat is lost to the container or surroundings.
What does a negative result mean?
Q is negative when the substance cools: it gives heat out. Cooling 0.5 kg of iron from 300 °C to 20 °C gives Q = 0.5 × 449 × (−280) = −62,860 J. In mixing mode the result is the heat that passes from the hotter to the colder substance.