an aircon system uses a refridegarant called r134a. this evaporates at -30c. there are two versions of the system. the one explained is the later version that will be on your 172.this is basically how it works:-
1,the r134a comes out of the compressor in gas form at about 10-15 bar pressure.
2,the r134a enters the condensor where it cools and condensors into liquid form.it then leaves the condensor in liquid form.
3,the r134a goes through a regulation valve on the bulkhead. as the r143a comes out of the other side of the valve the pressure drops to about 3 bar and the liquid goes into a droplet form.
4,the r134a now passes through the evaporator in droplet form. air is passed through fins on the evaporator before it enters the heater/air distribution box. as the air passes through it transfers its heat into the r134a (like a radiator but in reverse).
5,as the r134a absorbs the heat from the air it evaporates into a gas. the r134a leaves the evaporator in gas form.
6,the r134a passes back through a return channel on the regulator valve. the regulator valve has a sensing bulb on it that meassures the return r134a tempurature. this tempurature determines how much r134a the regulator lets into the evaporator in step 3.
7,the r134a goes through a cylinder unit called a reciever dryer. this removes any moisture from the r134a and collects any r134a that didnt evaporate. if r134a enters the compressor in liquid form it will damage the compressor.
8,the r134a leaves the reciever dryer and re-enters the compressor. the cycle goes back to step 1.
note- the compressor output is contolled by the aircon panel. it is a variable compressor so will stay on for most of the time as its output can be changed rather than just being an on/off compressor like on old systems. it will still completly turn off on full throttle though. compressor drive (the clutch) is activated by the injection computer after the aircon panel has requested it and all conditions are met eg-vehicle not on full throttle etc. the condensor is at the front of the car in front of the radiator. the compressor,regulator valve and reciever dryer are under the bonnet. the evaporator is inside the car or in the scuttle panel depending on model.