Thermodynamics and Steam
The first and second laws, ideal gases, steam tables, Rankine, Otto, Diesel and Brayton cycles, refrigeration and heat pumps, combustion and boilers, with worked numbers.
Thermodynamics is the science of energy: how heat and work convert into each other, why power stations, engines and refrigerators can only do so much, and how to calculate what they do. Steam is its most important working fluid, from the Rankine cycle of a power station to the process steam of a factory. This guide takes you from the first law and the properties of gases, through the second law and entropy, to steam tables, power cycles, refrigeration and heat pumps, combustion and boilers, and the practical side of steam systems. Every worked number is computed, and two cycles run through the pages: a 4 MPa steam plant and an R-134a refrigerator. The mechanisms of heat flow are in Heat Transfer, and the flow side in Fluid Mechanics and Pipe Flow.
Start here: what do you need?
| I need to… | Go to |
|---|---|
| use the first law, enthalpy and steady-flow equations | Properties, State and the First Law |
| calculate with air or another ideal gas, compressors and processes | Ideal Gases and Processes |
| find the maximum efficiency of an engine, or use entropy | The Second Law, Entropy and Carnot |
| read steam tables, find quality or latent heat | Steam, Water and Property Tables |
| analyze a steam power plant | Steam Power Cycles: Rankine |
| analyze a petrol, diesel or gas-turbine cycle | Gas Cycles: Otto, Diesel and Brayton |
| size a refrigeration cycle or heat pump | Refrigeration and Heat Pumps |
| work out air, fuel, flue loss and boiler efficiency | Combustion and Boiler Efficiency |
| size steam pipes, traps and condensate systems | Steam Systems, Traps and Troubleshooting |
A suggested order
Read Properties, State and the First Law and Ideal Gases and Processes first, then The Second Law, Entropy and Carnot for the limits. Steam, Water and Property Tables prepares for the cycles: Steam Power Cycles: Rankine, Gas Cycles: Otto, Diesel and Brayton and Refrigeration and Heat Pumps. The last two pages, Combustion and Boiler Efficiency and Steam Systems, Traps and Troubleshooting, are the practical side.
- Properties, State and the First Law: System and surroundings, state properties, work and heat, the first law for closed and open systems, enthalpy and steady-flow devices.
- Ideal Gases and Processes: The ideal gas law, specific heats, and the isothermal, isobaric, isochoric, adiabatic and polytropic processes with their work.
- The Second Law, Entropy and Carnot: Heat engines, the Kelvin–Planck and Clausius statements, entropy, the Carnot limit and isentropic efficiency.
- Steam, Water and Property Tables: Saturation, quality, superheat, how to read steam tables, interpolation and the boiling point against pressure.
- Steam Power Cycles: Rankine: The Rankine cycle step by step, efficiency, superheat, reheat, regeneration and a complete 4 MPa worked example.
- Gas Cycles: Otto, Diesel and Brayton: Air-standard cycles for petrol and diesel engines and gas turbines, compression ratio, efficiency and combined cycles.
- Refrigeration and Heat Pumps: The vapor-compression cycle, COP, the Carnot limit, refrigerant tables, and sizing a compressor with a worked R-134a example.
- Combustion and Boiler Efficiency: Air–fuel ratio, excess air, flue gas losses, heating values, condensing boilers and boiler efficiency.
- Steam Systems, Traps and Troubleshooting: Steam distribution, condensate, traps, flash steam, water hammer, insulation and a table of common problems.
Two cycles, two answers
Worked example: a power cycle and a refrigeration cycle
- A steam power plant (Steam Power Cycles: Rankine): steam at 4 MPa and 400 °C expands to 10 kPa, giving 1 066 kJ/kg from 3 018 kJ/kg of heat: 35.3 percent.
- A refrigerator (Refrigeration and Heat Pumps): R-134a between 0.14 and 0.8 MPa removes 144 kJ/kg for 36 kJ/kg of work: COP 3.97.
- Both follow the same recipe: draw the cycle, find the enthalpy at each state from tables, then add up the heat and work. The second law (The Second Law, Entropy and Carnot) says neither can reach the Carnot limit.
Quick reference: the equations
| What you need | Equation |
|---|---|
| First law, closed system | Q − W = ΔU |
| Steady-flow energy | Q̇ − Ẇ = ṁ (Δh + ΔKE + ΔPE) |
| Ideal gas | p V = m R T Δh = cp ΔT |
| Isentropic gas | T₂ ÷ T₁ = (p₂ ÷ p₁)(k−1)/k |
| Carnot efficiency | η = 1 − TC ÷ TH |
| Wet steam | h = hf + x hfg |
| Rankine efficiency | η = (wt − wp) ÷ qin |
| Otto efficiency | η = 1 − 1 ÷ rk−1 |
| Brayton efficiency | η = 1 − 1 ÷ rp(k−1)/k |
| COP | qL ÷ w (cooling), qH ÷ w (heating) |
| Boiler efficiency | η = 100 − Σ losses |
Related guides and tools
- Heat Transfer and Fluid Mechanics and Pipe Flow: the other two guides in this section.
- Psychrometric Calculator and Compressed Air Consumption Calculator.
- Pump Power and Sizing Calculator.
- The Pressure, Energy, Temperature and Power converters, and the Downloads library (a water-properties table and a thermodynamics formula sheet).
Safety first
- Steam and pressure equipment can kill. Boilers, steam lines and pressure vessels need design to the applicable code, safety valves, inspection and a competent person.
- Burns: steam, condensate and hot pipes burn at once; leaks may be invisible near the source.
- Combustion: carbon monoxide, fuel leaks and explosive mixtures. Keep burner safety systems, flues and ventilation working, and fit alarms.
- Refrigerants can be flammable, toxic or asphyxiating, and are regulated. Use qualified technicians.
- The numbers here are for study and preliminary design. Safety-critical and pressure systems need a competent engineer and the applicable codes.
FAQ
Where do I start with thermodynamics?
Read Properties, State and the First Law, then Steam, Water and Property Tables if you need steam.
Which steam tables should I use?
Any set based on IAPWS-IF97 (the textbook tables, the NIST WebBook, or free online calculators). Small differences between editions are not important for design.
Where are HVAC and psychrometrics?
They are the next guide in the Thermal and Fluids section; moist-air properties are already in the Psychrometric Calculator.
Why is thermodynamics hard?
Mostly because of the number of properties and tables. The trick is to draw the states, write down which properties you know at each, and apply the first law to each device.
References
- Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill; Moran, M. J., et al., Fundamentals of Engineering Thermodynamics, Wiley.
- Wagner, W., Kretzschmar, H.-J., International Steam Tables (IAPWS-IF97), Springer; NIST Chemistry WebBook.
- Heywood, J. B., Internal Combustion Engine Fundamentals; Boyce, M. P., Gas Turbine Engineering Handbook.
- ASHRAE Handbook – Fundamentals and Refrigeration; Spirax Sarco, Steam Engineering Tutorials; US DOE, Improving Steam System Performance.
Last reviewed: November 2026. Values are typical; check the standard, the manufacturer’s data and the code that applies to your system.