KEVOS® MAKEOS · Engineering
Vapour-Compression Refrigeration or Heat Pump Cycle Check (COP from State Enthalpies, Carnot Limit)
From the refrigerant enthalpies at the compressor inlet, isentropic discharge and condenser outlet, what refrigerant flow, compressor power and COP does this cycle give, how close is it to the Carnot limit, and does it meet the COP you need?
Single-stage vapour-compression refrigeration or heat-pump cycle from the refrigerant enthalpies at the compressor inlet, after isentropic compression and at the condenser outlet: the refrigerating effect, the actual compressor work, the heat rejected, the refrigerant flow and compressor power for the duty, the COP as a refrigerator and as a heat pump, and the comparison with the reversed-Carnot COP, against the COP you need.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty you are sizing for | choice | Cooling sizes the refrigerant flow on the heat absorbed; heating sizes it on the heat delivered. |
| Cooling or heating duty | kW | The cooling load (cooling) or the heat to be delivered (heating), from your load calculation. |
| Refrigerant state enthalpies (from tables or software, one reference state) | ||
| Enthalpy at the compressor inlet (evaporator outlet) | kJ/kg | Refrigerant enthalpy leaving the evaporator: saturated or superheated vapour at the evaporating pressure, from refrigerant tables or property software. |
| Enthalpy after isentropic compression to condensing pressure | kJ/kg | Enthalpy at the condensing pressure and the same entropy as the compressor inlet, from the superheated table or software. |
| Enthalpy at the condenser outlet (before the expansion valve) | kJ/kg | Enthalpy of the liquid leaving the condenser: saturated or subcooled liquid at the condensing pressure. |
| Compressor isentropic efficiency | % | Compressor isentropic efficiency from the compressor maker’s data at this pressure ratio. |
| Temperatures and target | ||
| Evaporating temperature | °C | Evaporating (saturation) temperature in the evaporator. |
| Condensing temperature | °C | Condensing (saturation) temperature in the condenser. |
| COP required for the selected duty | The COP the duty must reach, for example from the specification, an energy target or the existing plant. | |
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 you are sizing for
- What it is
- Whether the duty you enter is heat removed from the cold side (cooling) or heat delivered to the warm side (heating), which sets the COP reported and the refrigerant flow.
- Units and format
- Choose one of 2 options from the list: Cooling (refrigerator, chiller or air conditioner); Heating (heat pump).
- Example
- The form opens with “Cooling (refrigerator, chiller or air conditioner)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Switches the duty, the COP and the Carnot limit between the refrigerator and heat-pump forms.
- Get it right
- A reverse-cycle air conditioner is a heat pump when heating; enter the heating output in that case.
What this means: Cooling or heating duty
- What it is
- The rate of heat the system must remove (cooling) or deliver (heating), which fixes the refrigerant mass flow and compressor power.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Refrigerant flow, compressor power and both heat flows rise in proportion; COP does not change.
- Get it right
- Use the load at the design condition, including any safety allowance you normally add.
Refrigerant state enthalpies (from tables or software, one reference state)
What this means: Enthalpy at the compressor inlet (evaporator ou…
- What it is
- The specific enthalpy of the refrigerant vapour entering the compressor, at the evaporator outlet, including any superheat.
- Units and format
- Enter a number in kJ/kg: kJ/kg. The form accepts -500 kJ/kg to 3000 kJ/kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 395 kJ/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher value increases the refrigerating effect per kilogram for the same throttled liquid.
- Get it right
- Read it from the same table or program as the other two enthalpies; reference states differ between sources.
What this means: Enthalpy after isentropic compression to conden…
- What it is
- The enthalpy the refrigerant would have leaving an ideal compressor: at the condensing pressure and the same entropy as at the compressor inlet.
- Units and format
- Enter a number in kJ/kg: kJ/kg. The form accepts -500 kJ/kg to 3000 kJ/kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 425 kJ/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher value means more compressor work per kilogram and a lower COP.
- Get it right
- Find it in the superheated table at the condensing pressure using the inlet entropy, or with property software.
What this means: Enthalpy at the condenser outlet (before the ex…
- What it is
- The specific enthalpy of the liquid refrigerant leaving the condenser, which passes unchanged through the expansion valve into the evaporator.
- Units and format
- Enter a number in kJ/kg: kJ/kg. The form accepts -500 kJ/kg to 3000 kJ/kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 255 kJ/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower value raises the refrigerating effect and the COP.
- Get it right
- Subcooling lowers this value; use the liquid temperature measured before the valve where you can.
What this means: Compressor isentropic efficiency
- What it is
- The ideal (isentropic) compression work divided by the work the real compressor needs for the same pressure rise.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 20% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower efficiency raises the compressor work and discharge enthalpy and lowers the COP.
- Get it right
- Take it from the compressor maker’s data at your pressure ratio; it is not the motor efficiency.
Temperatures and target
What this means: Evaporating temperature
- What it is
- The saturation temperature of the refrigerant boiling in the evaporator, the cold end used for the reversed-Carnot COP.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 50 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -10 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raising it raises the reversed-Carnot COP, so the same cycle COP becomes a smaller share of the limit.
- Get it right
- Use the saturation temperature at the suction pressure, not the air or water temperature leaving the evaporator.
What this means: Condensing temperature
- What it is
- The saturation temperature of the refrigerant condensing in the condenser, the warm end used for the reversed-Carnot COP.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 150 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lowering it raises the reversed-Carnot COP, so the same cycle COP becomes a smaller share of the limit.
- Get it right
- Use the saturation temperature at the discharge pressure; it sits above the air or water it rejects heat to.
What this means: COP required for the selected duty
- What it is
- The coefficient of performance the selected duty must reach: heat moved per unit of compressor work, as a refrigerator or as a heat pump according to the duty chosen.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 50. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 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 of the COP check.
- Get it right
- Compare like with like: this cycle COP excludes motor, fan and pump power, so it is higher than a system rating.
Method and formulas
- Throttling is at constant enthalpy, so h₄ = h₃; refrigerating effect q_L = h₁ − h₄.
- Compressor work w = (h₂ₛ − h₁) ÷ η_c; actual discharge h₂ = h₁ + w; heat rejected q_H = h₂ − h₃ = q_L + w.
- COP_R = q_L ÷ w and COP_HP = q_H ÷ w; refrigerant flow ṁ = duty ÷ q_L (cooling) or duty ÷ q_H (heating); compressor power = ṁ w.
- Reversed-Carnot limits with T in kelvin: COP_R,max = T_L ÷ (T_H − T_L), COP_HP,max = T_H ÷ (T_H − T_L); second-law efficiency = COP ÷ COP_max.
- Example: enthalpies of 395, 425 and 255 kJ/kg with a 75 % compressor give a COP of 3.5 for cooling, 2.857 kW of compressor power and 0.0714 kg/s of refrigerant for 10 kW, 66.5 % of the reversed-Carnot COP of 5.263 between −10 °C and 40 °C.
Limitations
- One-stage cycle with an adiabatic compressor and expansion valve; no pressure drops in pipes and heat exchangers, no heat gains to the suction line, and no motor, drive or fan power. Real system COPs are lower.
- The enthalpies must come from one table or program with one reference state; mixing sources gives wrong results without any warning.
- A screening calculation, not a plant selection; the equipment maker’s data, AS/NZS 5149 and licensed refrigeration trades govern real systems.
- Example values are illustrations shaped like a common refrigerant cycle. Replace them with values for your refrigerant and conditions.
Typical uses
- Check a chiller, cold room or heat pump selection against a COP target
- Work out refrigerant mass flow and compressor power from a duty and refrigerant table values
- Show how much of the Carnot limit a real cycle reaches at a given lift
Who it is for
- Refrigeration and air-conditioning engineers and technicians
- Mechanical services designers
- Energy auditors
What you get
- Refrigerating effect, compressor work and heat rejected per kilogram
- Actual discharge enthalpy
- Refrigerant mass flow, compressor power and both heat flows
- COP as a refrigerator and heat pump, reversed-Carnot COP and second-law efficiency
- COP against the target
Interpreting the result
- The heat-pump COP is always the refrigerator COP plus one for the same cycle, because the compressor work also ends up as heat delivered.
- Each degree less lift between evaporating and condensing temperatures raises the Carnot COP, which is why clean condensers and correct evaporating temperatures save energy.
Before relying on the result
- Check the result against the compressor maker’s rated capacity and power at the same evaporating and condensing temperatures.
- Measure suction and discharge pressures and temperatures on the running plant to confirm the states assumed.
References
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach, 5th edition (McGraw-Hill, 2006), chapter 11 (sections 11-1 to 11-4: COP, reversed Carnot cycle, ideal and actual vapour-compression cycles) and section 6-12. Method reference; no tables, figures or examples are reproduced.
- AS/NZS 5149 Refrigerating systems and heat pumps: safety and environmental requirements (named by number and scope only).
- NIST Chemistry WebBook, thermophysical properties of fluid systems (webbook.nist.gov): one source of refrigerant enthalpies; note its reference state.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
The vapour-compression cycle
In Heat Pumps and Refrigeration by the Numbers
What it covers: Follow refrigerant around the vapour-compression cycle: evaporating, compressing, condensing and throttling, the energy balance, superheat and subcooling, and how faults show up.
Method explained here · KEVOS® original book
The vapour-compression cycle, point by point
In Process Chillers by the Numbers
What it covers: The four components and four states of CH-30's R-134a cycle from NIST data, refrigerant flow, compressor power, condenser heat and COP, the pressure–enthalpy diagram, and two reference states mixed.
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.