Sensible Heat for a Temperature Rise
Sensible Heat for a Temperature Rise
Heating a substance without changing its phase requires “sensible” heat. This worksheet computes the energy needed to raise a known mass through a temperature difference — the basis of water-heater, process-vessel and HVAC sizing.
The sensible-heat equation is Q = mcΔT, where m is the mass, c the specific heat capacity and ΔT the temperature rise.
Inputs
Heating 50 kg of water (c ≈ 4186 J/kg·K) by 30 K.
m := 50 kg=50 kg
c := 4186 J/(kg·K)=4186 m^2/K/s^2
dT := 30 K=30 K
Heat energy required
Q := m·c·dT=6.28e+06 Nm
Results
The result is the energy that must be added. Divide by the heating time to get the required power (Q/t = power), or by the burner/heater efficiency to get the fuel input. This ignores any phase change — boiling or melting would add latent heat on top.
Assumptions & limitations
- Specific heat constant over the temperature range.
- No phase change (sensible heat only).
- No heat loss to surroundings — add an efficiency factor in practice.