How do car air conditioners work?

The car air conditioner works the same way "regular" cyclic AC units do. A refrigerant in a vapor or gaseous state arrives at the compressor, which is mounted on brackets by the engine and is run by a belt, and gets compressed. This heats it up as well as increases its pressure - just as you'd expect according to standard gas laws. The hot gas (or vapor) is pumped to the AC condenser. The condenser is in the front of the car by the radiator for the engine coolant. The radiator and the AC condenser kinda look the same. Anyway, the outside air, which is either "pulled through" by a fan or forced through as the vehicle moves down the road, passes across the elements of the condenser and removes heat from them and, thereby, the refrigerant. From the condenser, the now-cooler refrigerant is handled by an expansion valve, and as the vapor comes out of this component, it is abruptly depressurized, which causes very rapid cooling. Again, basic gas law stuff. The cooled refrigerant changes phase to a liquid, and pressure in the system forces it on to and then through the evaporator inside the passenger compartment of the car. Here a fan blows vehicular inside air through the evaporator, and the really cold liquid refrigerant "soaks up" the heat in the air. Cold air is then blown out through the vents in the car to cool the passenger compartment. In the evaporator, the vapor in liquid form changes phase to a vapor as it absorbs thermal energy from the air being blown over it by the fan inside the duct work. From the evaporator, the refrigerant returns to the low pressure side of the AC compressor to begin the cycle anew. There are basic principles of thermodynamics at work here. When something is hot, it "sends" thermal energy out to a cooler place. If something is cool, it will "absorb" (or sink) heat. The greater the difference in temperature between the "hot" thing and the "cool" thing, the greater the "thermal pressure" to move heat. Simple and easy. Now add terms like temperature differential or thermal gradient to mean the difference in temperature, and a few other ones, and you'll be talking like a grad student defending his thesis!