Sensible Heat: Formula, Units and a Worked Boiler Example
Sensible heat is the heat that changes a substance’s temperature without changing its state. It is what a thermometer measures, what a feed tank gains from returning condensate, and what leaves a boiler through the stack.
You'll learn
- Define sensible heat and tell it apart from latent heat
- Use in both kJ and kcal
- Know why the specific heat of water is not exactly 4.18 at boiler temperatures
- Work out what warmer feedwater is worth in fuel
What sensible heat is
Put heat into water at 30 °C and its temperature rises. Keep going and it reaches its boiling point, and from there the temperature stops rising even though heat keeps going in: the heat is now turning water into steam. The first kind of heat, the kind that shows up as a change in temperature, is called sensible heat, because you can sense it with a thermometer. The second kind is latent heat, and it has a lesson of its own.
How much heat it takes depends on three things: how much of the substance there is, how far you want to raise its temperature, and what the substance is. Water takes a lot of heat to warm up; steel takes about a tenth as much for the same mass; air about a quarter. That property, how much heat one kilogram needs per degree, is called its specific heat.
Where you meet sensible heat in a boiler house
- Feedwater heating: the feed tank, the deaerator and the economizer all warm the water before it reaches the boiler, so the boiler has less to do.
- Stack loss: flue gas leaves the chimney hotter than the air that came in. The heat it carries away is sensible heat, and it is the largest single loss in most boilers.
- Thermic fluid heaters and hot water generators work on sensible heat alone. The fluid never boils; it gets hotter in the heater and cooler in the process.
- Start-up: tonnes of steel and water have to be brought up to temperature before a boiler makes any steam, which is why a cold start burns fuel for nothing.
The chart puts sensible heat in proportion. Of the 2,653 kJ it takes to make a kilogram of steam from cold water, only 651 kJ goes into raising the water to boiling point. The rest, about 75%, is latent heat.
The formula
| Symbol | Meaning | Unit |
|---|---|---|
| Heat added or removed | kJ (or kcal) | |
| Mass of the substance | kg | |
| Specific heat at constant pressure | kJ/(kg·K) | |
| Temperature change, final minus initial | K, or °C |
For a flow rather than a batch, replace the mass with a mass flow rate and the result is a heat rate: kg/h in, kJ/h out. Divide kJ/h by 3,600 for kW.
A temperature difference of 1 K is the same size as 1 °C, so can be worked in either. That is not true of temperatures themselves: anything that uses an absolute temperature, such as radiation or gas laws, needs kelvin.
Worked example: what warmer feedwater is worth
- A 5 TPH boiler at 10 kg/cm²(g), running at full load: 5,000 kg/h of feedwater.
- Feedwater today is cold make-up at 30 °C. Returning condensate to the feed tank would bring it to 80 °C.
- Heat the feedwater now gains in the tank instead of in the boiler, with = 4.18:
- Check against the steam table: water at 30 °C holds 126.7 kJ/kg and at 80 °C holds 335.8 kJ/kg, so the exact figure is 10,45,221 kJ/h. At these temperatures is within a fraction of a percent.
- In other units: 290 kW, or 2.5 lakh kcal/h.
- As a share of the boiler’s work: turning 30 °C water into saturated steam at 10 kg/cm²(g) takes 2,653.3 kJ/kg. The tank now supplies 209.0 kJ/kg of that.
Specific heat of water at boiler temperatures
The textbook value for water is 4.18 kJ/(kg·K), and near room temperature it is right. It is not constant, though. Computed from the IAPWS-IF97 formulation for water held at 10 kg/cm²(g), as it is inside a running boiler:
| Water temperature | , kJ/(kg·K) | , kcal/(kg·°C) |
|---|---|---|
| 20 °C | 4.18 | 0.999 |
| 50 °C | 4.18 | 0.998 |
| 80 °C | 4.19 | 1.002 |
| 100 °C | 4.21 | 1.007 |
| 120 °C | 4.24 | 1.014 |
| 150 °C | 4.31 | 1.029 |
| 180 °C | 4.41 | 1.052 |
Computed from IAPWS-IF97, region 1. Saturation at this pressure is 183.3 °C, so 180 °C is still liquid.
Between 20 and 100 °C the value barely moves. Above that it climbs, reaching 4.41 at 180 °C, about 5% more than 4.18. For a rough feedwater sum that error does not matter. For heating water to near its saturation temperature, or for an energy audit, use enthalpy from a steam table instead of ; the table already accounts for the change.
Other materials have much lower specific heats: plain carbon steel about 0.43 kJ/(kg·K) and air about 1.0, both near room temperature. Both also rise with temperature, and flue gas is not air: the water vapor in it has roughly twice the specific heat of air, so a wet fuel’s flue gas carries more heat per degree. That matters when a stack-loss calculation is the basis of an efficiency guarantee.
Why every 6 °C of feedwater is worth about 1% of fuel
The rule of thumb you will hear on site falls straight out of the energy balance. The fuel a boiler burns is proportional to the heat it adds to each kilogram of water, from feedwater enthalpy up to steam enthalpy, so the fraction saved by warmer feedwater is:
| Symbol | Meaning | Unit |
|---|---|---|
| Enthalpy of feedwater before the improvement | kJ/kg | |
| Enthalpy of feedwater after it | kJ/kg | |
| Enthalpy of the steam produced | kJ/kg |
From 30 to 36 °C at 10 kg/cm²(g) that gives 0.94%. The rule holds because the denominator, the total heat to make steam, is about 2,653 kJ/kg, while each 6 °C step adds only about 25. It assumes boiler efficiency stays the same. That is close to true when the feedwater is warmed by something outside the boiler, such as returned condensate. On a boiler with an economizer it is not: warmer water entering the economizer cools the flue gas less, the stack runs hotter, and part of the saving is lost.
Key takeaways
- Sensible heat changes temperature, not state: .
- For water, is close to 4.18 kJ/(kg·K) up to 100 °C and rises to about 4.4 at 180 °C. Near saturation, use steam table enthalpies.
- 1 kcal = 4.1868 kJ. Never mix the two inside one calculation.
- Every 6 °C of feedwater temperature is worth roughly 1% of boiler fuel.