KEVOS® MAKEOS · Engineering
Heat Pump and Chiller COP Check (Carnot Limit, Second-Law Efficiency, Running Cost)
Is the COP claimed or measured for this heat pump or chiller possible at these temperatures, how close is it to the Carnot limit, and what does it cost to run?
Check of a heat pump or chiller’s coefficient of performance against the second law: evaporating and condensing temperatures from the source and sink temperatures and the approach temperatures you enter, the Carnot (reversible) COP for heating or cooling, the actual COP from the duty and electrical input, the second-law efficiency, the yearly electricity cost, and the input power at your minimum efficiency, against the Carnot limit and the minimum efficiency you accept.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | choice | Whether the useful output is heat delivered (heat pump) or heat removed (chiller). |
| Source (cold-side) temperature | °C | Temperature of the cold side: outdoor air or ground for a heat pump, chilled water or the cold room for a chiller. |
| Sink (hot-side) temperature | °C | Temperature of the hot side: heating water for a heat pump, condenser air or cooling water for a chiller. |
| Evaporator approach (source minus evaporating) | K | How far the evaporating refrigerant runs below the source (from the unit’s design data). |
| Condenser approach (condensing minus sink) | K | How far the condensing refrigerant runs above the sink. |
| Performance and cost | ||
| Duty (heating or cooling output) | kW | Rated or measured heating or cooling output at these temperatures. |
| Electrical input | kW | Rated or measured electrical input at the same condition. |
| Lowest second-law efficiency accepted | % | Lowest share of the Carnot COP you accept as realistic for this kind of unit (your own benchmark). |
| Electricity price (incl. GST) | AUD/kWh | Electricity price including GST, or ex GST for a GST-registered business. |
| Running hours per year | h/year | Running hours at this duty per year. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Duty
- What it is
- Whether the useful output is the heat delivered on the hot side, as for a heat pump, or the heat taken from the cold side, as for a chiller.
- Units and format
- Choose one of 2 options from the list: Heating (heat delivered to the sink); Cooling (heat taken from the source).
- Example
- The form opens with “Heating (heat delivered to the sink)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Switches between the heating and cooling Carnot COP.
- Get it right
- A heat pump’s Carnot COP is always one more than a chiller’s at the same temperatures; choose the duty you are rating.
What this means: Source (cold-side) temperature
- What it is
- The temperature of the cold side the machine draws heat from: outdoor air or ground for a heat pump, the chilled water or cold room for a chiller.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 200 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A warmer source reduces the temperature lift and raises the Carnot COP.
- Get it right
- Use the temperature at the rated condition you are checking, not an annual average.
What this means: Sink (hot-side) temperature
- What it is
- The temperature of the hot side the machine rejects heat into: the heating water for a heat pump, or the condenser air or cooling water for a chiller.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 300 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter sink increases the lift and lowers the Carnot COP.
- Get it right
- For heating water use the flow temperature leaving the heat pump.
What this means: Evaporator approach (source minus evaporating)
- What it is
- How many degrees the evaporating refrigerant runs below the source temperature, the approach the evaporator needs to take in heat.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0 K to 50 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger approach lowers the evaporating temperature and the Carnot COP.
- Get it right
- Take it from the unit’s design data; a fouled or iced evaporator increases it.
What this means: Condenser approach (condensing minus sink)
- What it is
- How many degrees the condensing refrigerant runs above the sink temperature, the approach the condenser needs to reject heat.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0 K to 50 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger approach raises the condensing temperature and lowers the Carnot COP.
- Get it right
- Take it from the unit’s design data; a dirty condenser coil increases it.
Performance and cost
What this means: Duty (heating or cooling output)
- What it is
- The heating or cooling output of the machine at the stated temperatures, rated or measured.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The actual COP and second-law efficiency rise in proportion.
- Get it right
- Use output and input from the same test condition; mixing a rated output with a measured input gives a meaningless COP.
What this means: Electrical input
- What it is
- The electrical power drawn by the machine at the same condition as the output, including the compressor and any fans or pumps the rating includes.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher input lowers the COP and raises the running cost.
- Get it right
- Include the same auxiliaries the rating includes; leaving out fans flatters the COP.
What this means: Lowest second-law efficiency accepted
- What it is
- The lowest share of the Carnot COP you accept as realistic for this type of machine, your benchmark for judging the claim.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the input power at that efficiency.
- Get it right
- Set it from your own experience or independent test data; this tool does not give a value.
What this means: Electricity price (incl. GST)
- What it is
- The cost of one kilowatt-hour of electricity to the site, used for the yearly running cost.
- Units and format
- Enter a number in AUD/kWh: Australian dollars per kilowatt-hour. The form accepts 0 AUD/kWh to 100 AUD/kWh. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 AUD/kWh as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly running cost rises in proportion.
- Get it right
- State whether it includes GST; a GST-registered business normally works ex GST.
What this means: Running hours per year
- What it is
- The number of hours a year the machine runs at this duty, used for the yearly running cost.
- Units and format
- Enter a number in h/year: h/year. The form accepts 0 h/year to 8784 h/year. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 h/year as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yearly running cost rises in proportion.
- Get it right
- Use equivalent full-load hours; part-load running at lower input counts for less.
Method and formulas
- Evaporating T_e = source − evaporator approach; condensing T_c = sink + condenser approach (kelvin).
- Carnot COP: heating T_c ÷ (T_c − T_e), cooling T_e ÷ (T_c − T_e), the reversed Carnot cycle (Fermi eqs 58–60).
- Actual COP = duty ÷ input; second-law efficiency = actual ÷ Carnot; yearly cost = input × hours × price; input at the minimum efficiency = duty ÷ (minimum × Carnot COP).
- Example: Carnot COP 6.7323, actual 3.3333, a second-law efficiency of 49.513 % and A$9,000 a year.
Limitations
- Uses the refrigerant’s evaporating and condensing temperatures from your approach values; a unit tested to a standard rating condition must be compared at that condition.
- Steady-state duty only: defrost, part-load cycling, pumps and fans outside the measured input are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Test a supplier’s COP claim before buying a heat pump or chiller
- Check a measured COP after commissioning
- Show how lowering the sink temperature cuts running cost
Who it is for
- Mechanical and building services engineers
- Energy managers
- Plant engineers
What you get
- Evaporating and condensing temperatures
- Carnot COP and actual COP
- Second-law efficiency
- Yearly running cost and input power at your minimum efficiency
Interpreting the result
- The Carnot COP depends on the temperature lift, so a heat pump delivering 35 °C water rather than 55 °C can use markedly less power for the same heat.
References
- Fermi E., Thermodynamics (Dover Publications, 1956; first published by Prentice-Hall, 1937), pp. 31–45. Method reference; no text, examples or tables are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Temperature lift and approach
In Process Chillers by the Numbers
What it covers: How evaporating and condensing temperatures drive capacity, power and COP, approach temperatures, setpoints and head pressure, and a dirty condenser coil.
Method explained here · KEVOS® original book
Heat pumps and refrigerators against the limit
What it covers: Carnot limits for cooling and heating COPs, why temperature lift dominates performance, the extra headroom when water is heated from cold, and how to spot an impossible COP.
Method explained here · KEVOS® original book
COP and the Carnot limit
In Heat Pumps and Refrigeration by the Numbers
What it covers: Define 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.
Method explained here · KEVOS® original book
Safety, fume, cooling and the hour rate
In Laser Processing by the Numbers
What it covers: Laser classes and guarding, fume extraction duct checks, chiller duty in hot weather, the machine hour rate of a laser cutter, quoting on full machine time, and the cell's process record.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.