Formula & Calculator
Sensible Heat Duty
Calculates the heat required to change the temperature of a stream without a phase change.
Interpretation
Sensible heat duty: Q = m·c_p·ΔT, heat to change temperature without phase change. Example: Heating 2 kg water from 20 to 80°C, c_p=4.18 → Q=501.6 kJ.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Q | Heat duty | kW |
| m | Mass flow rate | kg/s |
| cp | Specific heat capacity | kJ/kg.K |
| dT | Temperature change | K |
What it means
Sensible heat is the heat added to or removed from a substance to change its temperature without changing its phase. The required heat duty Q is calculated as Q = m c_p ΔT, where m is mass, c_p is the specific heat capacity at constant pressure, and ΔT is the temperature change. This formula is used extensively in heating and cooling processes, such as in heat exchangers, reactors, and building HVAC systems. It is also used to size heaters and coolers. The specific heat capacity is material‑dependent and varies with temperature, though often taken as constant over small ranges. In chemical engineering, sensible heat calculations are a routine part of energy balances. They are also used in environmental engineering to assess thermal pollution. Understanding sensible heat is fundamental for designing efficient thermal systems and for complying with energy regulations.
Worked example
Sensible Heat Duty – Two Examples
Real‑World| Parameter | Value |
|---|---|
| m | 2 kg/s |
| cp | 4.18 kJ/kgK |
| ΔT | 20 K |
| Parameter | Value |
|---|---|
| m | 1 |
| cp | 2.0 |
| ΔT | 50 |
Common mistakes
- Mass m: In kg – not moles.
- Specific heat c_p: In J/(kg·K) or kJ/(kg·K) – be consistent with Q.
- Temperature difference ΔT: In K or °C (same magnitude).
- No phase change: This formula is for sensible heat only; if phase change occurs, add latent heat.
- Average c_p: If c_p varies with T, use the average over the temperature range.
Applications
Sensible heat duty, Q = m·c_p·ΔT, is the heat required to change the temperature of a substance without phase change. It is used in countless heating and cooling applications, from process heaters and chillers to building HVAC systems. Engineers calculate sensible heat to size heat exchangers, to determine utility requirements, and to perform energy balances. The specific heat capacity c_p is temperature‑dependent, but averaged values are often used. This formula is also applied in the design of solar thermal systems, food processing, and metallurgical operations. By accurately estimating sensible heat, professionals can ensure that thermal equipment meets process needs while optimising energy consumption and cost.
- Sizing of heat exchangers for heating and cooling duties
- Energy balance calculations for chemical processes
- Design of HVAC systems and building heating loads
- Thermal analysis of reactors, furnaces, and ovens
- Selection of heat transfer fluids and utility systems
Frequently Asked Questions
Sensible heat duty is the heat required to change the temperature of a stream without a phase change: Q = ṁ · c_p · ΔT, where ṁ is the mass flow rate, c_p is the specific heat at constant pressure, and ΔT is the temperature change. This is used for heating or cooling liquids and gases.
- Assuming c_p is constant over the temperature range – it varies, especially for gases.
- Using the wrong specific heat (e.g., c_v instead of c_p).
- Not converting units – ensure ṁ (kg/s), c_p (J/kg·K), ΔT (K) give W.
- Ignoring latent heat when a phase change occurs.
Use an average c_p over the temperature range, or integrate Q = ṁ · ∫ c_p(T) dT. Polynomial expressions for c_p(T) are common in thermodynamics.
Sensible heat changes temperature; latent heat changes phase (melting, boiling) at constant temperature. Both are part of the total heat duty.
Use the mass‑weighted average c_p of the mixture: c_p,mix = Σ y_i·c_p,i (mass fraction) or Σ x_i·c_p,i (mole fraction) depending on the basis. Then apply Q = ṁ·c_p,mix·ΔT.
Watts (W) or kilowatts (kW) for power; Joules (J) for total energy. In imperial, Btu/h or Btu.
- Design of heaters and coolers.
- Sizing of heat exchangers.
- Energy balance calculations.
- Thermal design of reactors.