The machine and its pressure–enthalpy chart, side by side and always in step. Set the temperatures, pick a process to light up both at once, and read where the COP comes from.
Mode
Duty
Units
Refrigerant
Vapour-compression cycle
— R-134a, 5.0 to 45.0 °C
Chart layers
Process
Pick a process to light it up on the machine and on the chart at the same time — or press Walk the cycle to step through all four in order.
COP (cooling)
4.52
Of Carnot
65%
Cooling
5.00 kW
Comp. power
1.11 kW
Heat rejected
6.11 kW
Quality at 4
25.5%
COP = q evap / w = 153.4 / 33.9 = 4.52
R-134a between 5.0 and 45.0 degrees Celsius. Coefficient of performance 4.52, which is 65 percent of the Carnot limit. Refrigerating effect 153.4 kilojoules per kilogram, compressor work 33.9. Quality after the valve 25 percent.
Drag state 1 or state 3 on the chart. Sideways changes superheat or subcooling; up and down changes the evaporating or condensing temperature. With the chart focused, press 1 or 3 to choose a state and move it with the arrow keys — Shift moves ten steps at a time.
Six presets, each one a machine you have met. The note explains why its numbers are what they are.
The two temperatures
5.0 °C
45.0 °C
The machine
5 K
8 K
75%
85%
5.0 kW
The four states
State
Where
P (kPa)
T (°C)
h (kJ/kg)
s (kJ/kg·K)
Phase
1
Compressor suction
350
13.0
409.8
1.7543
superheated vapour
2
Compressor discharge
1160
65.6
443.8
1.7796
superheated vapour
3
Condenser outlet
1160
40.0
256.4
1.1926
subcooled liquid
4
Evaporator inlet
350
5.0
256.4
1.2030
two-phase · x = 25.5%
Mass flow
0.0326 kg/s
Pressure ratio
3.32
Discharge temp.
65.6 °C
Swept volume
136.3 L/min
Carnot COP
6.95
Refrigeration tonnes
1.42 TR
All six at these conditions
Ranked by COP, recomputed every time you move anything. Notice how little separates them — and how much the other columns differ.
Refrigerant
COP
Pressure ratio
Discharge (°C)
Swept vol. (L/min)
GWP
Safety
R-134a
4.52
3.32
65.6
136.3
1430
A1
R-290
4.51
2.78
69.6
102.2
3
A3
R-22
4.49
2.96
86.9
88.1
1810
A1
R-717
4.44
3.45
135.6
79.8
0
B2L
R-32
4.31
2.92
94.8
55.3
675
A2L
R-410A
4.24
2.89
89.5
59.0
2088
A1
Practice
0 of 0
Loading a question…
The stage above is showing the cycle the question is about, with the answer blurred out. Read it off the chart — that is the exercise.
Question 1 of 5
0 correct
The equations, with your numbers in them
Six relations, evaluated at the cycle on screen right now. Nothing here is a fitted shortcut — these are the definitions.
Refrigerating effect — the width of the bottom line
qevap = h1 − h4—
Compressor work — ideal work over isentropic efficiency
w = (h2s − h1) / ηis—
Coefficient of performance
COP = qevap / w—
Carnot limit — absolute temperatures, always
COPmax = Tevap / (Tcond − Tevap)—
Quality after the valve — because h4 = h3
x4 = (h4 − hf) / hfg—
Mass flow — what turns kJ/kg into kW
ṁ = Q̇ / qevap—
—
Link copied.The link carries the refrigerant, both temperatures and the whole machine, in plain readable parameters.
How to read a refrigeration cycle on a P–h chart
1Set the two temperatures that decide almost everything: how cold the evaporator has to run, and how hot the condenser can get. The gap between them is the lift, and the lift is what the compressor is paid to overcome.
2Read the cycle as a rectangle on the chart. The bottom edge is evaporation and its width is the refrigerating effect; the right edge leaning over is compression and its width is the work; the top is condensation; the vertical drop on the left is the expansion valve.
3Divide those two widths and you have the COP. The readout writes the division out, so you can check it against the chart rather than trust it.
4Add subcooling to widen the bottom edge at no extra work, and superheat to watch the discharge temperature climb while the COP barely moves. These are two different knobs that look similar and are not.
5Switch refrigerant to see how little the COP changes and how much the pressure, discharge temperature and compressor size do — then switch to heating to read the same machine as a heat pump.
What a refrigeration cycle is, and why it needs a chart
A refrigerator does not make cold. It moves heat from a place that is already cold to a place that is already warm — the direction heat will never travel on its own — and the compressor is what pays for that violation. Everything else in the loop exists to return the refrigerant to a state where it can absorb heat again. That is why the machine is a loop and not a line, and why the same four components appear in a domestic fridge, a car's air conditioning, a supermarket cold room and an air-source heat pump.
The trick that makes it work is the phase change. A boiling liquid absorbs enormous amounts of heat at constant temperature, and a condensing vapour releases it again the same way. So the cycle is arranged to boil the refrigerant where you want heat removed, and condense it where you do not mind heat appearing. The expansion valve and the compressor are simply the two devices that shuttle it between the pressures at which those two things happen at the right temperatures.
A pressure–enthalpy chart exists because that story is otherwise invisible. Plot pressure up the side and specific enthalpy across the bottom, and each of the four processes becomes a line with a distinctive shape: flat along the bottom for evaporation, leaning up the right for compression, flat across the top for condensation, and straight down the left for the throttle. The widths of two of those lines are the only numbers you need for the COP. An engineer who can read one of these can answer in seconds a question that otherwise needs a page of property-table lookups.
The four processes, and what each one costs
Every component in the loop is one line on the chart, and the shape of the line is what the component does.
Compression is the only work input. An ideal compressor rides a line of constant entropy; a real one ends further to the right, and that gap is work that turned into heat in the gas rather than into pressure. Divide the ideal width by the real one and you have the isentropic efficiency.
Condensation is flat, and it carries everything. The heat leaving here is everything absorbed in the evaporator plus everything the compressor put in — which is why the schematic can print the sum and have it balance exactly.
Expansion is vertical, and it is a pure loss. A throttle takes out no work and lets in no heat, so the enthalpy cannot change. Pressure and temperature both collapse and part of the liquid flash-boils, arriving at the evaporator already spent. It is the one process here that destroys usable work and produces nothing.
Evaporation is flat, and its width is the whole point. This is the refrigerating effect — the heat each kilogram of refrigerant removes from the cold space. Divide it by the compression width and you have the COP.
Because those shapes are so distinct, a cycle is usually easier to diagnose by eye than by arithmetic. A compressor that is tired, a condenser that is dirty, a valve that is overfeeding — each of them deforms the rectangle in its own recognisable way.
Refrigerants, and what actually decides the choice
Refrigerant selection has been driven for three decades by environmental constraints stacked on top of thermodynamic ones. Ozone depletion potential removed the CFCs and then the HCFCs; global warming potential is now removing the HFCs. What is often lost in that story is that efficiency was rarely the deciding factor — at the same evaporating and condensing temperatures, the fluids below sit within a few percent of one another.
Refrigerant
ODP
GWP
Typical use
Note
R-12
1
10,200
Refrigerators and car AC before 1994
Banned in new equipment from 1996 under the Montreal Protocol.
R-22 ·
0.055
1,810
Older split AC, supermarket packs
Production ended in the EU in 2010 and the US in 2020.
R-134a ·
0
1,430
Car AC 1994–2017, centrifugal chillers
No ozone impact, but banned in new EU car AC from 2017.
R-410A ·
0
2,088
Residential AC and heat pumps
Runs 50–60% above R-22 pressure. Now being phased down.
R-32 ·
0
675
Modern split AC
Half the GWP of R-410A, and mildly flammable (A2L).
R-1234yf
0
4
Car AC after 2017
Mildly flammable. The Kigali-era replacement for R-134a.
R-290 ·
0
3
Domestic refrigerators, small heat pumps
Flammable (A3), so charge limits are what keep installations safe.
R-744
0
1
Transcritical commercial refrigeration
Critical point is only 31 °C, so warm-weather cycles run transcritical.
R-717 ·
0
0
Industrial refrigeration, ice rinks
The best thermodynamics on this list, and toxic (B2L).
The six marked with a dot are the ones this simulator can run. What separates them in practice is not COP but operating pressure, discharge temperature, how large a compressor a given duty needs, flammability, toxicity and GWP — and those trade against each other. Ammonia has the best thermodynamics and is toxic. Propane is excellent and flammable. R-32 halves R-410A's GWP and is mildly flammable. There is no fluid that wins on every axis, which is precisely why the argument has run for thirty years.
Who this is for, and what it is not
It is built for the people who need the cycle in front of them rather than in a textbook: mechanical and building-services students working through refrigeration and air-conditioning courses, HVAC and process engineers checking a duty or a discharge temperature, and anyone trying to understand why their air conditioner struggles in May. The Practice and Quiz modes exist because reading a P–h chart is a skill that comes from doing it, not from being shown it once — and the chart deliberately stays on screen in both, because a question about a chart should not be asked with the chart hidden.
It is a teaching and checking instrument. Saturation pressures come from Wagner correlations fitted to published tables and hold within a few tenths of a percent; latent heat uses the Watson relation and holds within about two percent; the superheated vapour is treated with an effective constant specific heat, which means the discharge temperature carries a few kelvin of model error while the COP does not. All six fluids share one enthalpy datum, so absolute enthalpies may be offset from your textbook even though every difference reported here is unaffected. Cite the ASHRAE Handbook or REFPROP in a report; use this to understand the answer, and to catch the times a number does not look right.
Frequently Asked Questions
What are the four processes in a vapour-compression refrigeration cycle?
Four components, four processes, one loop. The compressor raises low-pressure vapour to condensing pressure — the only work input, and the denominator of the COP. The condenser rejects that heat plus the heat picked up in the cold space, at constant pressure. The expansion valve throttles the liquid back down, doing no work and exchanging no heat, so the enthalpy cannot change. The evaporator boils the cold mixture at constant pressure, absorbing heat from whatever is being cooled. On a pressure–enthalpy chart those four draw as a rough rectangle: flat along the bottom, leaning up the right, flat across the top, and straight down the left.
What is COP, and what is a good value?
The coefficient of performance is the useful heat moved divided by the work paid for — COP = qevap / wcomp when cooling. It is dimensionless and it is routinely greater than one, because a refrigerator does not make cold, it moves heat. Typical figures: a domestic refrigerator lands near 2, a room air conditioner between 3 and 4, and a chiller with a small temperature lift can pass 5. A deep freezer at −30 °C drops to about 1.5, purely because the lift is so much larger. The ceiling is the Carnot COP, Tevap / (Tcond − Tevap) in kelvin, and a real cycle reaches roughly 40–60% of it.
Why does the expansion valve draw as a vertical line?
Because throttling is isenthalpic. The valve extracts no work and, over the few centimetres it occupies, exchanges essentially no heat — so with nothing entering or leaving, the enthalpy of the refrigerant on the way out equals the enthalpy on the way in. On a chart whose horizontal axis is enthalpy, an unchanged enthalpy is a vertical line. What does change is pressure, and with it temperature: the liquid arrives warm and high-pressure and leaves as a cold two-phase mixture, part of it having flash-boiled on the way through. That flash is the reason state 4 sits inside the saturation dome rather than on its left edge.
Does subcooling improve COP? Does superheat?
They do different things and it is easy to confuse them. Subcooling — cooling the liquid below its condensing temperature — moves state 3, and therefore state 4, to the left. That widens the evaporator line and adds refrigerating effect for no extra compressor work, so the COP genuinely rises: on the default cycle, 15 K of subcooling is worth a few percent. Superheat mostly does not. It moves state 1 to the right, but it moves state 2 by almost the same amount, so the COP barely shifts — what climbs steeply is the discharge temperature. Superheat exists to guarantee no liquid reaches the compressor, not to buy efficiency.
Which refrigerant gives the best COP?
At the same evaporating and condensing temperatures, far less separates them than the marketing suggests. Run all six through the comparison in the tool and the COPs typically fall inside a 15% band — the fluid choice is worth a few percent, while moving the temperatures is worth a factor of three. What genuinely differs is everything else: R-32 and R-410A need the smallest compressor for a given duty because their vapour is dense, R-717 (ammonia) needs the least mass flow but runs the hottest discharge by a wide margin, and R-290 (propane) is excellent thermodynamically and flammable. Refrigerant selection is a decision about pressure, discharge temperature, compressor size, safety class and GWP — not about a COP league table.
What is the difference between COP, EER and SEER?
They measure the same ratio in different clothes. COP is dimensionless — watts of cooling per watt of electricity — at one rated operating point. EER is the same ratio in mixed units, Btu per hour of cooling per watt of input, so EER ≈ COP × 3.412. SEER is a seasonal average weighted across a synthetic cooling season, which is why it is higher than the rated COP: real systems spend most of their hours at part load and small lift, where efficiency is best. India's ISEER is the same idea on a CSPF basis using Indian climate bins, and it is what the BEE star rating on an air conditioner is calculated from.
How is a heat pump different from a refrigerator?
Thermodynamically, not at all — it is the same four components in the same loop. The only difference is which end you care about. A refrigerator's useful output is the heat removed at the evaporator; a heat pump's is the heat delivered at the condenser. Since the condenser must reject everything the evaporator absorbed plus the compressor work, the heating COP is always exactly one more than the cooling COP: COPheating = COPcooling + 1. Switch the tool to Heating and you can watch that hold on every setting. It is also why a heat pump delivering 4 kW of heat for 1 kW of electricity is not breaking any law — three of those kilowatts were outside, and it only paid to move them.
Why does an air conditioner get worse on a hot day?
Because the condenser has to sit above ambient to reject heat at all. When the outdoor air goes from 35 °C to 45 °C the condensing temperature follows it up, the pressure ratio rises, the compressor works harder per kilogram, and the throttling loss grows because the liquid entering the valve is hotter — so more of it flashes to vapour and less is left to do useful boiling. Every one of those pushes the same way. On the default cycle here, moving the condenser from 45 °C to 55 °C costs roughly a fifth of the COP, and it happens on precisely the afternoon when the cooling load is highest.
What does quality at state 4 tell you?
Quality is the mass fraction that is vapour, and at state 4 it is the fraction of your refrigerant that flash-boiled crossing the expansion valve without cooling anything. A quality of 0.30 means 30% of the flow arrives at the evaporator already evaporated and contributes nothing to the refrigerating effect. Lower is better, and the two ways to lower it are more subcooling — which moves state 4 left, deeper into the dome — and a smaller temperature lift. It is one of the clearest things to watch on the chart: drag the subcooling up and the left-hand vertical slides bodily leftward.
Why is the pressure axis logarithmic?
Because a refrigeration cycle spans a pressure ratio of about 3 to 12, and on a linear axis the evaporator line would be pressed flat against the bottom of the plot where nothing could be read off it. A logarithmic axis gives the low-pressure half of the cycle the same vertical room as the high-pressure half. It has a second benefit that is not cosmetic: the pressure ratio, which is what actually determines how hard the compressor is working, becomes a distance on the chart — the same ratio occupies the same height wherever it sits.
How accurate is this model?
Saturation pressures come from Wagner correlations fitted to published tables and hold within 0.3% for the pure fluids and 0.6% for R-410A, which is a blend with a small temperature glide this model does not represent. Latent heat uses the Watson relation and holds within about 2%. The superheated vapour is treated with an effective constant specific heat, which is the model's real limitation: discharge temperature carries a few kelvin of error, while discharge enthalpy — and therefore COP — does not. All six fluids share one enthalpy datum (IIR: 200 kJ/kg for saturated liquid at 0 °C), so absolute enthalpies may be offset from your textbook even though every difference the tool reports is unaffected. It is a teaching instrument, not a substitute for REFPROP or the ASHRAE Handbook.