Lessons · Engineering · sensible heat, Q = m c ΔT
Sensible heat: how much energy to change a temperature
Heating a mass m of a material with specific heat c by ΔT takes Q = m c ΔT. For water, c is about 4186 J/(kg·K).
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A client wants a 200 L tank of water taken from 15 °C to 40 °C in half an hour and asks for a 2 kW heater. Q = m c ΔT says that needs about 11.6 kW, so the heater is a sixth of what is needed, and it is better to say so in the meeting than after the first cold shower.
How to think about it
Mass in kilograms, the material's c, the temperature rise in kelvin or Celsius, which is the same size. Multiply. Divide the energy by a heater's power for the time it takes.
Worked example
Q = m c ΔTHeat is mass times specific heat times temperature change.
Warm 3 kg of water from 15 °C to 65 °C; c = 4186 J/(kg·K)The rise is 50 °C, and a degree Celsius is the same size as a kelvin.
Q = 3 × 4186 × 50 = 627,900 J = 628 kJAbout six hundred kilojoules.
On a 2 kW heater: t = 627,900 / 2000 = 314 s, about 5 minutesEnergy over power is time.
Your turn
2.5 kg of water, 20 °C to 60 °C. Write the heat.
Q = 2.5 × 4186 × = 418,600 J
Solve one, graded on the server
The trap
Using water's c for a steel tank. Steel's c is about 490 J/(kg·K), a ninth of water's, so the same heat warms steel nine times as much. Look the material up; do not guess it.