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How to use
Use this specific heat and temperature change calculator to solve Q=m·c·ΔT for heat energy Q, mass m, specific heat capacity c or temperature change ΔT. It can therefore act as a temperature-change calculator when Q, m and c are known, or as a heat-release calculator when cooling makes Q and ΔT negative.
- Choose the quantity to solve for.
- Enter the other three values and select energy, mass and c units.
- Calculate the solved quantity and normalized values.
How it is calculated
Example
Example: heating 1kg of water from about 20°C to 100°C with c=4186 J/(kg·K) gives ΔT=80K and Q=334,880J.
Important notes
Q=mcΔT describes sensible heating or cooling without a phase change. Melting, boiling or condensation requires latent heat, and real specific heat can vary with material and temperature.
Worked examples and interpreting results
Assume specific heat 500 J/(kg·K), mass 2 kg and a temperature rise of 10 K. Required energy is 10000 J, provided the material does not change phase and specific heat remains constant.
| Case | Calculation | Result |
|---|---|---|
| Energy for a 10 K rise | 2 × 500 × 10 | 10,000 J |
| Energy for a 20 K rise | 2 × 500 × 20 | 20,000 J |
How to check the result
A difference of 10 K equals a difference of 10°C; do not add 273.15 to a temperature difference. The example assumes c without assigning it to a material. Phase changes require a separate latent-heat calculation.
Specific heat equation Q = mcΔT: worked examples
Sensible heat Q equals mass m times specific heat capacity c times temperature change ΔT. Keep units consistent: kilograms, joules per kilogram per degree and the temperature difference produce joules.
- Heat for 2 kg, c=4180, 10-degree rise: 2 × 4180 × 10 = 83,600 J
- Mass from 1000 J, c=500 and 4-degree rise: 1000 ÷ (500 × 4) = 0.5 kg
- Temperature change from Q=5000, m=2, c=500: 5000 ÷ (2 × 500) = 5 °C
Important note
The formula assumes no phase change and roughly constant specific heat capacity across the temperature interval. Melting and vaporization require latent-heat treatment.
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Frequently asked questions
How do I calculate temperature change?
Rearrange Q=m·c·ΔT to ΔT=Q/(m·c). Enter heat energy, mass and specific heat capacity and the calculator solves the temperature change.
Is a °C temperature difference equal to K?
Yes. Temperature differences have the same numerical size in °C and K.
How do I calculate heat released during cooling?
Use Q=m·c·ΔT. With the sign convention used here, cooling gives a negative ΔT and therefore a negative Q; the magnitude is the heat released.
Why can Q be negative?
Cooling releases heat, so ΔT and Q can be negative while m and c remain positive.
Does the formula include melting or boiling?
No. Q=mcΔT describes temperature change within one phase using an appropriate specific heat. A phase change requires latent heat, and specific heat itself may vary with temperature.