Sensible Heat (Q = mcΔT)
Also known as Q = mcΔT · Q = m cp ΔT · mcp delta T · specific heat equation · calorimetry equation · heat energy formula
Worked example: 2 kg water, c = 4186, ΔT = 30 C° → 251160 J — press Try an example to run it live, then adjust anything.
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Sensible Heat (Q = mcΔT) explained
Sensible heat is the energy that changes a substance's temperature without changing its phase. The specific heat capacity c is the price of each degree: how many joules one kilogram demands per kelvin of warming. Water's is famously steep at about 4186 J/(kg·K), which is why oceans moderate coastal climates and why a kettle takes its time. Heating 1.5 kg of water from 15 °C to 95 °C costs Q = 1.5 × 4186 × 80 ≈ 502 kJ.
The concept dates to Joseph Black's calorimetry experiments in 1760s Glasgow, which first pried apart the ideas of temperature and heat. Note that ΔT is a temperature difference, so a change of 80 °C equals a change of 80 K exactly — Fahrenheit differences convert by scale alone, with no offset. The formula holds as long as c stays roughly constant over the range and nothing melts or boils along the way.
Sensible Heat (Q = mcΔT) formula
- = Heat energy (J)
- = Mass (kg)
- = Specific heat capacity (J/(kg·K))
- = Temperature change (C°)
Missing one of these? Work it out first, then come back
- Heat energy — Kinetic Energy, Thermal Efficiency
- Mass — Newton's Second Law, Kinetic Energy
- Specific heat capacity — Stream Duty from Mass Flow (Q = ṁcΔT), Prandtl Number
- Temperature change — Thermal Linear Expansion, Calorimeter Heat (q = C_cal ΔT)