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Heat Pumps and Refrigeration by the Numbers
The second law, COP, the vapour-compression cycle, heat pump water heating, cold room loads, compressors and refrigerant rules, in one food factory
Use the second law to judge heat pumps and refrigeration: Carnot limits, COP, the vapour-compression cycle, heat pump water heating, cold room loads, compressor energy and refrigerant rules.
Start readingAbout this book
Refrigerators, air conditioners, heat pumps and air compressors all do one thing that heat will not do by itself: they move heat, or energy, in a direction it would not flow naturally, and they pay for it in electricity. How much they must pay is limited by the second law of thermodynamics, and the limit depends almost entirely on temperatures. That makes these machines unusually predictable by numbers: a few temperatures tell you the best a machine could possibly do, and a realistic fraction of that best tells you what to expect. The same numbers explain why a dirty condenser costs money, why a heat pump that is efficient for warm water is poor for very hot water, and why a cold room’s door discipline matters.
This book works these machines through by numbers. It starts with the second law and the Carnot limits, defines the coefficient of performance, walks through the vapour-compression cycle, evaluates a heat pump for a factory’s hot water, builds up a cold room’s refrigeration load, explains what drives running costs, applies the same thinking to air compressors and their waste heat, and finishes with the rules for refrigerants. Each chapter works one question through the running case, shows a failure and how it was found, and ends with an exercise and its worked answer.
The running case
The book follows two pieces of plant at a fictional food factory, the same factory whose hot water and steam systems appear in Heat Transfer by the Numbers and Process Steam by the Numbers. The first is a proposal to supply part of the wash-down hot water system’s heat, about 150,000 kWh a year at up to 85 °C, from a heat pump instead of gas. The second is CS-1, a chilled store held at 2 °C, 6 m by 5 m by 3 m, receiving about 2,000 kg of product a day.
All quantities, prices and results are invented for teaching. This is an illustration. None of it describes a KEVOS® client, supplier or project. Heat from gas is costed at about A$0.093 per kWh delivered, as in the companion books, and electricity at an assumed A$0.25 per kWh. Money is in Australian dollars, excluding GST. Real machines’ performance comes from their makers’ data at the actual operating conditions; this book’s ratio of real to ideal performance, 0.5, is a teaching value.
How to use the book
Chapters 1 to 3 build the ideas: the second law, COP and the cycle. Chapters 4 and 5 apply them to the two pieces of plant. Chapter 6 covers running costs and maintenance, Chapter 7 compressed air and heat recovery, and Chapter 8 refrigerants and safety.
Source limits and professional responsibility
The supplied thermodynamics notes informed the range of subjects. The methods here are standard thermodynamics, simplified for hand calculation, with sources for material data. Refrigerating systems and heat pumps are regulated: handling fluorocarbon refrigerants requires a licence, and system design and installation follow the applicable standards and work health and safety law. Some refrigerants are flammable or toxic. Real systems must be designed, installed and serviced by appropriately licensed and competent people. This book is educational and is not a design manual.
Who this book is for
Plant and maintenance engineers, energy managers, facility managers and owners who buy, run or evaluate refrigeration, heat pumps and compressors in factories and commercial buildings.
What you will learn
- Explain the second law in practical terms and calculate the Carnot limits for engines, refrigerators and heat pumps.
- Estimate a realistic COP from temperatures and see how temperature lift drives running cost.
- Compare a heat pump with gas water heating on running cost, and design a sensible hybrid.
- Build up a cold room's refrigeration load and size the plant from it.
- Calculate the ideal energy to compress air, find recoverable heat, and know the rules for handling refrigerants.
Inside this book
Chapters
- 01The second law and its limitsUnderstand the second law in practical terms: heat flows downhill, entropy and irreversibility, the Carnot limit on turning heat into work, energy quality, and checking claims against the limit.
- 02COP and the Carnot limitDefine the coefficient of performance for cooling and heating, calculate its Carnot limit from two temperatures, estimate realistic COPs, and see why temperature lift drives the cost of moving heat.
- 03The vapour-compression cycleFollow refrigerant around the vapour-compression cycle: evaporating, compressing, condensing and throttling, the energy balance, superheat and subcooling, and how faults show up.
- 04Heat pump water heatingEvaluate a heat pump for factory hot water: COP at each temperature, why heating all the way to 85 °C costs more than gas, hybrid preheating, a waste-water source, and paybacks under different prices.
- 05Cold room loadsBuild up a chilled store's refrigeration load from walls, floor, product, door infiltration and internal heat, size the plant from the daily total, and find the loads worth reducing.
- 06Running refrigeration efficientlyKeep a refrigeration plant's lift small and its COP high: clean condensers and evaporators, condenser placement, defrost, set points, controls and a maintenance routine, with the cost of each fault.
- 07Compressors and recovered heatCalculate the ideal work to compress air, see why real compressors use more and why staging with intercooling helps, and recover the heat that nearly all compressor power becomes.
- 08Refrigerants, rules and safetyUnderstand refrigerant families and their hazards, the licensing and legal frame for handling them in Australia, leak management, cold room and plant safety, and refrigerant choice.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Explained in this book
Heat Engine and Heat Pump Second-Law Check (Carnot Limit, Entropy Generated, Lost Work)
Calculates the Carnot COP for cooling or heating from two temperatures and the share of it a stated COP reaches.
Used in COP and the Carnot limit, The second law and its limits
Explained in this book
Heat Pump, Chiller or Heat Engine Claim Check (Carnot Limit, Second-Law Efficiency, Running Cost)
Calculates the Carnot COP for heating or cooling from two temperatures, the actual COP from output and input, and their ratio.
Used in COP and the Carnot limit
Applies this method
Heat Engine Carnot Limit Check (Ideal Efficiency, Second-Law Efficiency, Most Work, Least Heat Rejected)
Checks a heat engine or heat-to-power claim against the Carnot efficiency this chapter derives, and shows the work and heat rejected it implies.
Used in The second law and its limits
Applies this method
Heat Pump and Chiller COP Check (Carnot Limit, Second-Law Efficiency, Running Cost)
Calculates the Carnot COP for heating or cooling from the evaporating and condensing temperatures and compares a rated or measured COP with it.
Used in COP and the Carnot limit
Applies this method
Vapour-Compression Refrigeration or Heat Pump Cycle Check (COP from State Enthalpies, Carnot Limit)
Calculates the cycle’s energy balance: heat absorbed, compressor work, heat rejected and COP, from refrigerant enthalpies.
Used in The vapour-compression cycle
Related Tools and Examples
Useful alongside
Steam Rankine Cycle Check (Efficiency, Steam Flow, Heat Rate, Turbine Exhaust Dryness)
Works a real steam cycle: its efficiency, condenser duty and steam flow, well below the Carnot ceiling this chapter sets for steam.
Related to The second law and its limits
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 27 October 2026.
- University course notes; the supplied file does not state the author. Introduction to Thermodynamics with Applications (about 2004). Supplied source, read as a subject map of entropy and the second law, entropy accounting, power and refrigeration cycles and steady-flow devices. It is a modern copyright work; no text, figures, examples or problems are reproduced. This book's case, calculations and figures are original.
- The Engineering ToolBox. Thermal Conductivity of Common Materials (current web page). Source for the conductivity of polyurethane foam, 0.03 W/m·K, used for the cold room panels in Chapter 5.
- Australian Refrigeration Council. Frequently Asked Questions (current web page). Background for Chapter 8: handling fluorocarbon refrigerants requires a refrigerant handling licence issued by the ARC on behalf of the Australian Government; other refrigerants may have other requirements.
- Commonwealth of Australia; Standards Australia and Standards New Zealand. Ozone Protection and Synthetic Greenhouse Gas Management Act 1989, and AS/NZS 5149, Refrigerating systems and heat pumps: safety and environmental requirements (as amended; current edition). Named by title and scope only, in Chapter 8, as the legislative and standards frame for refrigerants and refrigerating systems. No provisions are quoted.
- Safe Work Australia. Model Code of Practice: Managing the risks of plant in the workplace (current edition). Background for the plant safety points in Chapter 8. Check whether the code has legal effect in your jurisdiction.