The Laws of Thermodynamics and Entropy, for Boiler Engineers
Four short laws govern every boiler. The first says energy is never lost, only moved, which is why a boiler can be audited. The second says heat only flows downhill and never turns fully into work, which is why stacks are hot and condensate must be removed. Entropy is the quantity that keeps score.
You'll learn
- State the laws of thermodynamics in boiler-house terms
- Write an energy balance for a boiler
- Work out the Carnot limit and say what it means for steam
- Read entropy in a steam table and check it against latent heat
Before this: Enthalpy
The four laws, in plain words
- Zeroth law: two things each at the same temperature as a third are at the same temperature as each other. It sounds obvious, and it is what makes a thermometer meaningful.
- First law: energy is neither created nor destroyed. Every kilocalorie in the fuel ends up somewhere: in the steam, up the stack, in the ash, or radiated from the shell.
- Second law: heat flows on its own only from hot to cold, and no engine can turn all of the heat it takes in into work. Some must always be rejected to something colder.
- Third law: nothing can be cooled to absolute zero. It sets the zero of the kelvin scale and rarely troubles a boiler house.
What the first two laws mean on site
The first law is why a boiler can be audited. If the fuel’s heat must all go somewhere, then measuring where it goes, and how much is lost on the way, tells you the efficiency. The indirect method of efficiency testing is the first law written out as a list of losses.
The second law is behind three everyday facts. A heat exchanger needs the steam hotter than the product, or no heat moves. A stack is always warmer than the air, because flue gas can only be cooled towards the temperature of whatever it gives its heat to. And a boiler making steam for a turbine can only ever turn a fraction of its heat into power; the rest has to be rejected.
The energy balance
| Symbol | Meaning | Unit |
|---|---|---|
| Boiler efficiency | — | |
| Steam flow | kg/h | |
| Fuel burned | kg/h | |
| GCV | Gross calorific value of the fuel | kJ/kg |
Measuring the top and bottom of that fraction directly is the direct method. Measuring each loss and subtracting from 100% is the indirect method. Both rest on the same law; they differ in what is easier to measure accurately.
The Carnot limit
| Symbol | Meaning | Unit |
|---|---|---|
| Temperature heat is taken in at | K | |
| Temperature heat is rejected at | K |
- Steam at 10 kg/cm²(g) is at 183.3 °C (456.5 K). Heat is rejected at 30 °C (303.2 K).
- Temperatures in kelvin, always:
Entropy, and checking it in the steam tables
Entropy is the quantity the second law is written in. Heat added at absolute temperature raises a body’s entropy by , and in any real process the total entropy of everything involved goes up. A heat exchanger with a large temperature difference generates more entropy, and wastes more of the steam’s ability to do useful work, than one with a small difference.
Boiling happens at constant temperature, so the latent heat divided by the absolute saturation temperature should give the entropy of evaporation. At 10 kg/cm²(g): = 2,002.1 ÷ 456.49 = 4.3859 kJ/(kg·K). The steam table, computed independently, lists = 6.5577 − 2.1718 = 4.3859. The two agree, which is a useful check on any table you are handed.
Where entropy earns its keep in industry is turbines. An ideal turbine expands steam at constant entropy, so a back-pressure turbine in a sugar or paper mill is sized by following a line of constant entropy from inlet to exhaust and reading the enthalpy drop. The real machine falls short of that line, and the shortfall is its isentropic efficiency.
Key takeaways
- First law: every unit of fuel heat goes somewhere, which is what makes efficiency auditable.
- Second law: heat flows only from hot to cold, and never turns fully into work.
- The Carnot limit at 10 kg/cm²(g) and 30 °C is about 34%: steam this hot is better for heating than for power.
- Entropy of evaporation equals latent heat divided by absolute saturation temperature.