A quick test to see if you a regas will sort inop ac is to unscrew one of black port caps and activate the valve with a blunt instrument (lolly pop stick works great)
If you have pressure a fast jet of gas will be expelled and the system should work great again with a service/re-gas, if not then nothing will happen and your issue is greater than a service. make sure to keep body/skin out of harms way of escaping gas and be very quick as it will be clear if the system is pressurised
A few things on this: the contents are really, really nasty so use eye protection if you try it. If you have no pressure, that certainly indicates the system has lost all of its gas. If that's the case, a pro will probably try to pull a vacuum on the system over 10-20 mins and see if there is a leak. If there's nothing obvious, they may suggest adding a UV dye plus nitrogen gas to see if the leak can be spotted and rectified. On the other hand, if it holds a vacuum, they'll go straight in with a re-gas.
Top leak suspects:
Condenser (the A/C radiator that sits in front of the engine cooling radiator: this is by far the most common. You can easily see it from the front, esp with the bonnet off: often they'll be visibility distorted or corroded.
O-rings: these can split. They are the green AC system rings, different from the various black standard ones you can find. Still cheap though.
Compressor seals: particularly on rarely used / serviced systems.
Pipe corrosion. When these systems go for long periods without servicing or perhaps just have the squirty top-ups, acid builds up and can corrode fitting from the inside out. This is one good reason for having regular services to the AC system.
If the above test reveals pressure, it might suggest that at least the system holds pressure: although it doesn't tell you how much. You'd only need 5 psi or so to be able to hear a hiss, but the system pressure might be 30Psi upwards. It might be that actually, as soon as you ask the system to take more, it starts to leak. Nevertheless, residual pressure is normally a good sign. It doesn't necessarily mean it'll work though: you might still have high or low pressure sensor faults, compressor clutch issue, external temperature sensor faulty / damaged / missing (esp in accident repaired cars).
For all that ... as I mentioned before, lots of people will refund you if the system can't be recharged so it's always worth giving it a go if nothing is obviously wrong.
Sorry, I know we said this thread would finish with the alternator, but I couldn't resist chiming in (again
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