Since the thermal efficiency of this process is 82%, dividing 12 by .82 gives a new specific enthalpy of 14.6 Btu/pound.
Using 185 (the original starting point) we add 14.6 to get 199.6, or about 200 Btu/lb
Re-plotting the compression line below the new discharge temperature emerges. (Temperature lines are in 10 degree increments).

Sub-cooling serves several purposes, two of which are to ensure a solid stream of liquid gets to the metering device, and increase the refrigeration effect.
So, why is a solid column of liquid required? Performance of the metering device will be greatly reduced. All metering devices will only meet their rated capacity while being provided all liquid at a specified pressure drop. If a metering device gets liquid and flash gas the performance suffers greatly. The valve will hunt for set point, and the system pressures will behave erratically which could lead to other control problems.
Only liquid droplets can evaporate and remove latent heat from the load. Flash gas is already boiled liquid so there is no latent energy potential to pick up the load in the evaporator. A metering device, in its simplest form, can be considered an orifice (plate with a hole in it). In the illustration below, the upper would be something like an orifice getting full liquid pushed against the plate and developing large droplets to feed the evaporator. The lower orifice is getting a mix of gas and liquid emitting a spray of gas and tiny droplets which will be inefficient at removing the heat energy in the evaporator.
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On the pressure-enthalpy diagram, sub-cooling occurs in the final stage of the condenser then continues, to a lesser extent, in the liquid line until it reaches the metering device. The diagram shows what 10 degrees of liquid sub-cooling looks like on a R-410a cooling cycle.
The chart also shows nearly a 10 Btu/pound loss of capacity because the specific enthalpy difference is now less. 10 Btu/lb loss on a cycle that is 70 Btu/lb would be a little over 14%.
​

Another point to consider is how much sub-cooling is enough? This can be found using the pressure enthalpy diagram and the piping information. Line-sets, filter dryers, friction loss, and condenser pressure drop all add up to give a total pressure loss on the high-side of the system.
The diagram below has 5 degrees of sub-cooling marked against 10 psi incremental pressure drops. After 20 psi the metering device will start getting flash gas. 20 psi seems like a lot of pressure loss, but add it up, 80 equivalent foot of 3/8 liquid line (50 linear foot and three elbows) has a pressure loss of about 10 psi, filter dryer 3 psi, leaving 7 psi for the condenser, that’s cutting it close.
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A sub-cooling of 10 degrees allows for almost 40 psi pressure drop before failing at the valve. Most recommendations for split systems are rarely less than 9 degrees of sub-cooling.
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The unit is a 400 ton, R-134a, four-stage compressor, with a two-stage flash gas economizer. To perform a heat balance and diagnose a condenser problem, the total flow of refrigerant through the condenser needs to be known.
The full flow through the condenser is the sum of the evaporator and the compressor side loads from the economizer.
The gas in the economizer is part liquid, part vapor, the vapor goes to the compressor, the liquid proceeds toward the evaporator.
Multi-stage compressors have an ability to introduce gas in between impellor stages. This gas is taken from the economizer which lowers the pressure in the economizer stage, the result is an increase in refrigeration effect and a reduction of heat exchange surface area (which reduces first costs, maintenance costs, and is very desirable).
Below is a basic arrangement of the two-stage economizer and four-stage compressor system (no valves or controls are shown). The arrows mark the basic direction of flow and the numbered points mark the location of where the data points are associated with the points on the pressure enthalpy diagram (next figure).
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The first step is to determine the mass flow of refrigerant through the evaporator. The unit is a 400-ton unit, to find the mass flow of refrigerant multiply 400 X 200 Btu/minute/per ton, and divide by the enthalpy difference between point 1, and point 12, or, 163 – 73 = 90 Btu/pound/minute, so (400 X 200)/90 = 888.8 pounds per minute.
889 pounds per minute are flowing through the evaporator (I rounded up), we can now determine the ratio of the pounds of flash gas to pounds of liquid in the low side from the enthalpy values at points 11, 12, and 4 as follows:
(Point 11 – Point 12)/ (Point 4 – Point 11), or (83 – 73)/ (165 – 83) = .122
To find the flash gas flow multiply .122 by 889 to get, 108.5 pound per minute of flow for the flash gas from the low side economizer.
Next step is to find the flow from the high side economizer.
The flow is cumulative through the compressor, so, our new flow is 889 + 108.5 = 997.5 pound per minute to the third stage.
We need to find the ratio of gas to liquid again using the same approach except this time using points, 10, 11, and 7. (Point 10 – Point 11)/ (Point 7 – Point 10) = (101 – 83) / (171 – 101) = .257
Using the flow of 997.5 multiplied by .257 we get, 256 pounds per minute flow from the high side economizer.
So, to find the full flow to the condenser, 889 + 108.5 + 256 = 1253.5 pounds of refrigerant per minute through the condenser.
Note: Point 3 and 6 are internal to the compressor and not likely obtainable in the field, since you have the two ratios needed now, the points can be found using the pressure enthalpy diagram as follows:
Point 3 = (Point 2 enthalpy + (low side ratio X Point 4 enthalpy))/ (1 + (low side ratio))
Point 3 = (169 + (.122 X 165))/ (1 + .122) = 168.6
Point 6 = (Point 5 enthalpy + (high side ratio X Point 7 enthalpy))/ (1 + (high side ratio))
Point 6 = (176 + (.257 X 171))/ (1 + .257) = 174.9
Point 3 and point 6 are in reasonable agreement to the design information with error likely attributed to me reading the scaling on the chart.
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You are working on a 2-ton air-cooled condenser using 410a refrigerant. The system just almost cools the load but, there seems to be a capacity problem and low sub-cooling (difference between the actual liquid line temperature and the saturation temperature of the refrigerant), so, you suspect a condenser problem.
The condenser is a little dirty, but the fan appears to be moving air okay. There is some fin damage, and the condensing fan looks like it has been changed recently, so you want to investigate if the condenser is moving enough air.
This is a 2-ton unit, so, it is cooling 400 Btu/min. The system is designed for 100-degree Fahrenheit condensing temperature while operating a 45-degree Fahrenheit evaporator.
We need to know the mass flow of the refrigerant, per minute, moving through the system. We plotted the cycle diagram on the pressure-enthalpy diagram and dropped lines from the points of interest straight down to the enthalpy scale. Below is what we ended up with:
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The specific enthalpy of the evaporator, or refrigerant effect, is the difference between 182 Btu/lbm and 108 Btu/lbm, or, 74 Btu/lbm. This is all the cooling the evaporator was designed for, so, if we are getting 400 Btu/min of cooling from the system, we must be moving, 400÷74=5.4 lbm of refrigerant.
The specific enthalpy of the condenser is 192-108=84 Btu/lbm. Multiplied by our mass flow, 84X5.4=453.6 Btu/min of total heat-rejection for the condenser.
We now have a basic model of how our system was intended to operate, from this, finding the condenser air-flow is straight forward.
First convert the condenser heat to Btu/hour by multiplying by 60 minutes, 435.6X60=27,216 Btu/hour heat rejection.
Next, we need to know the temperature difference from the condenser discharge and the ambient air. In the field, we would just take this measurement, for discussion we will use the “apparent” rise from the pressure enthalpy chart. I marked the chart up to find the temperature difference of the refrigerant cycle in orange below.
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The chart is a little crowded at the top, but you can make out that the lines end on 120 and 90 degrees Fahrenheit, or a temperature difference of 30 degrees. We don’t know the exact temperatures of the air from the chart, but the difference will be proportional.
Next, we use the formula CFMX1.08X(T2-T1) =Btu/hour. We want to know CFM (cubic foot per minute) for our condenser fan, so, we must re-arrange the formula to solve for CFM, or, (Btu/hour)/ (1.08XTemperature difference)
Solving: 27216/(1.08X30) =840 cubic foot per minute of condenser air minimum.
With the flow known, 840cfm, the condenser air flow can be tested and determined whether it is sufficient enough to reach capacity. 
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Once the refrigeration machine has been leak pressure tested, repaired, and dehydrated, now comes the moment of truth…The Standing Vacuum Test!
​With all the other checks and tests combined, there is no other method that positively, beyond a show of doubt, proves a system is dry and tight. (If the test is properly performed).
You perform a standing vacuum test in lieu of the 24-hour standing vacuum test or the 24-hour temperature compensated standing pressure test because simple monitoring of the system the first couple of hours will tell you what you need to know once you know what to look for.
The standing vacuum test, is a test, it doesn’t benefit the mechanical procedure, nor dry the machine, it’s value is that of time and expense.
You perform the test using a vacuum pump that can achieve anything below 500 microns, the bigger the pump, the faster it will pull down, assuming you properly dehydrated the system prior to this step. (See Rapid Dehydration.)
Once the system has reached a vacuum of 1000 microns, or less, isolate the system with a digital vacuum gauge attached to it1. Begin plotting your readings over time on the chart below every 10 minutes.

The chart is a plot of the vapor pressure of water (light blue) and ice (dark blue) evaporating in a vacuum over time. The first point you will make will be at the “Minutes 0” (far left side) and the appropriate pressure (somewhere below a 1000 microns).
As the minutes’ progress, continue to plot the readings from the digital vacuum tester and a “trend” will emerge, a trend is just a line displaying the direction the test is going, a flat horizontal line for 90 minutes would be outstanding results, but what you will likely see looks like the chart below:
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At “0 Minutes”, the system was isolated at a pressure of 500 microns. Once data was plotted, up to 45 minutes, the line trended up a little, then got steady at 800 microns and continued there for the duration of the test. This would be an example of a good test. The early trend up was the system reaching equilibrium from the deep vacuum and some extremely small, but acceptable, amount of moisture, once at 800 microns, the vacuum holds. This is a good vacuum and pretty dry system. The vacuum level should be below 1000 micron for most systems, some systems (capillary tubes) should be taken to 500 microns2.
Below are some other ways the test could go.
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If your trend starts upward at a fairly steep incline, like the yellow line, the system still has a leak. The steeper the upward trend, the bigger the leak.
If your trend slowly progresses up and then follows the pitch of the blue lines, like the red line above, the system is wet. When the vacuum is first shut off, and the system isolated, there is a brief period of stabilization when the atmosphere in the system reaches equilibrium (balances out). After that, the trend follows the vapor pressure (blue line) until the final level of moisture is reached, once there, the trend will flatten out at the final pressure and remain there, the value of the flat part is the final vacuum level and moisture level. A system in this condition needs further dehydrate. A system that has standing water will follow the blue line.
So, a short system test can alleviate the 24-hour standing vacuum test that some recommend and can prevent putting a system into service that still has problems.
1.      Use only a digital vacuum gauge that can be attached and left on the system. You do not want to disturb the vacuum in any way during the test. Do not use a wet bulb device or other fluid filled thermometers.
2.      Always use the evacuation and dehydration levels recommended by the manufacturer.
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A persistent, methodic, and patient person will find a leak in a refrigeration system before anyone else. It may seem like it takes a long time, but it doesn’t hold a candle to the time involved with repeated evacuation and pressure testing, especially if the system is very large.
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The following is an outline of how to approach leak testing to save time and effort.
     1.      Have a planned approach. Use a sketch of the system to mark the progress as you go. Start at one point and work along the system path, this prevents repetitive checking. Mark the sketch up as you go, for instance, note a section you can’t get at to test or got small hits, because once you eliminate the known area, the leak must be in the unknown area.
     2.      Know the tricks. Use tape to isolate flanged connections, wrap the connection and poke a small hole, this way you are testing one point rather than the entire flange. Another trick, test insulation at seams, the refrigerant will propagate under the insulation until it finds a way out. Look for oil, if there is oil stain there is a leak at some point. Put balloons over relief devices and plug the weep hole to find a slow leak valve. Put condenser or chilled water straight from the chiller in a closed container and let it sit, after a while use an electronic detector to sense if any residual refrigerant is in the container, could be a tube leak.
     3.      Use tags, chalk, or any removable marker to note leaks on the system as you go. Do not use paint or permanent markers because once the leak is repaired, the tag or mark needs removed.
     4.      Pick the right tool for the job and know how it works. There are many leak detection tools, and they all work, but there isn’t any one tool that will do it all.

I have listed the leak detection tools that I’m aware of below, they are not in any order, just as they occurred to me.
     Ø  Bubble solution: This can be homemade from dish-soap and water, or, commercially available, such as SNOOP®. It works by coating the area with a high surface tension fluid, when the gas seeps out of the pipe it is momentarily captured by the fluid and a bubble forms then pops. This is a tried and true method of testing for leaks. Couple draw-backs; it can freeze, and you do get liquid all over the place when you use it.

     Ø  Foaming shave cream: When applied to a leak, the gas will leave a little hole in the cream or blow it off completely. It also works well to find leaks on long seams or where a solution won’t hang long enough. Can find leaks on vacuum or pressure. Draw-backs; Is messy and short lived sometimes drying up or breaking before small leaks are found. Aerosol cans may not be permitted on premises and it isn’t good if its windy out.

     Ø  Ultra-sonic leak detectors: Several are available and all generally work to “listen” for the high frequency sound that occurs when gas leaks out. They are used by narrowing the search area based on the pitch, volume, or number of beeps increasing as you search. These can help isolate a leak in a wall. Draw-backs; they don’t work well in noisy or windy environments and lack the ability to “pin-point” a leak. If there are numerous leaks, you will hear them all.

     Ø  Sniffers: Or, electronic gas detectors, are designed to pick up trace amounts of gas in an air stream. They work by using a little air pump to pull samples across an LED light, a receiver, tuned to the specific frequency of the gas, compares the sample to its reference and alarms when it gets a match. These can be very accurate and are usually easy to use, hand held, and fairly rugged, but they have some draw-backs; get water or oil in the end and your done until you replace the filter. They will pick up false hits if you move too fast or get too close. They take a second or so to register a leak, so move slow.

     Ø  Halide and sniffers that use heated elements: they work, but do so by burning the sample. Draw-back; I avoid these since you don’t always know if there is a flammable atmosphere which could lead to an explosion.

     Ø  Helium leak detectors: These detectors work by identifying helium atoms in a sample stream, you can’t fool them, at least not ones that work on gas chromatograph basis. They will find the smallest leak possible. Draw-backs; the detectors are expensive, you need a supply of helium to add to the system, they are costly to maintain.

     Ø  Thermal imaging leak detectors: These are relatively new to the industry. Based, in part, on the fact that there will be a temperature drop associated with the leak. There is an image of the equipment you watch through a screen looking for the temperature zone that’s out of place, there’s the leak. Draw-backs; they are very expensive and costly to maintain/repair. If you have ever tried to take a picture of every aspect and all sides of a system, then you know how challenging these would be to maneuver in a congested mechanical room.

There are all kinds of ways to find leaks and new ones are invented every day. If you know of a clever way to spot a leak, please let me know!

​Stall is when a centrifugal compressor reaches a point of maximum flow and minimum head. The wheel can deliver no more gas. (For a description of the centrifugal wheel and head, see “Centrifugal Refrigeration Compressor Surge”.)
Stall is common in aircraft engines, turbo-chargers, and other turbo machinery that operate in an open loop, but much less likely to occur in a closed loop refrigeration machine.
A theoretical wheel curve is displayed bellow, the far-right line labeled “stall”, is at the operating conditions the compressor must reach to induce “stall”.

​For a refrigeration machine to reach the conditions at stall on the graph above, there would need to be almost no head across the compressor, and a flow, far exceeding the design.
Refrigeration machines are closed loop systems, take a vacuum cleaner and stick the suction nozzle into the discharge port, wa-la, closed loop system, if you kept the motor cool, the vacuum would run and run and never see a stall condition.
Now, I agree, not a fair comparison, vacuum cleaner and refrigeration machine, but the point is clear, without a mechanism to induce more volume flow into the loop, the flow can’t exceed what the compressor is capable of.
It is true, that a great deal of volume can be generated by the boiling of the refrigerant in the evaporator, and it does, but not more than the machine is designed to handle.
I guess you could have huge evaporator that, at times, gets overloaded, and is piped up to a compressor that runs forward on the curve, with a ginormous condenser that sits in the arctic; I just have never come across such a design or miss-applied machine to witness this perfect storm. However, if you have I would love to hear about it.