Here is how all the various parts of a car's air conditioning works:
Compressor: The compressor is the core part of the air conditioning system, powered by a drive belt connected to the crankshaft of the engine. When the aircon system is turned on, the compressor pumps refrigerant vapour under high pressure to the condenser.
Condenser: The condenser is a device used to change the high-pressure refrigerant vapor to a liquid. It is mounted in front of the engine's radiator, and it looks very similar to a radiator. The vapour is condensed to a liquid because of the high pressure that is driving it in, and this generates a great deal of heat. The heat is then in turn removed from the condenser by air flowing through the condenser on the outside.
Receiver: The now liquid refrigerant moves to the receiver-dryer. This is a small reservoir vessel for the liquid refrigerant, and removes any moisture that may have leaked into the refrigerant. Moisture in the system causes havoc, with ice crystals causing blockages and mechanical damage.
Expansion Valve: The pressurised refrigerant flows from the receiver-drier to the expansion valve. The valve removes pressure from the liquid refrigerant so that it can expand and become refrigerant vapour in the evaporator.
Evaporator: The evaporator is another device that looks similar to a car radiator. It has tubes and fins and is usually mounted inside the passenger compartment behind the fascia above the footwell. As the cold low-pressure refrigerant is passed into the evaporator, it vaporises and absorbs heat from the air in the passenger compartment. The blower fan inside the passenger compartment pushes air over the outside of the evaporator, so cold air is circulated inside the car. On the 'air-side' of the evaporator, the moisture in the air is reduced, and the 'condensate' is collected and drained away.
Compressor: The compressor then draws in the low-pressure refrigerant vapour to start another refrigeration cycle. The refrigeration cycle then runs continuously, and is regulated by the setting of the expansion valve.
The whole process is reasonably simple when explained like that. All air conditioning systems work on the same principle, even if the exact components used may vary slightly between car manufacturers.
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