There are many processes in this world that seem like they would work but don’t because of the relationship between the amount of energy generated that is available to do the work and the amount of energy required to actually do the work are not in the proper relationship.
As an example if you take a liter bottle of diet soda and drop a couple of Mentoes tabs into it you will get a violent reaction. To the casual observer the aggressive jet of soda from the bottle might seem like a good candidate for a means of propulsion, but the student of engineering knows that even though we see an impressive release of energy in this reaction that amount of energy is going to need to be greater than the energy required to overcome the mass of the liter of soda and start it moving.
When you start to see things in rational terms relative to the processes that they control or are part of (cause and affect) you get a whole new view of the world. The 3G v6 has a 3 liter engine, it inhales air of that volume every few revolutions. In the very simplest terms take that volume and using your knowledge of 4 cycle operation, factor in the gear ratio for the average speed you are driving and you can get a formula to calculate the volume of air that your engine uses in a minute. With that knowledge you can then turn to the problem of figuring how long it takes to cool that volume of air X degrees from ambient.
By ambient I mean the temperature of the air from where you are getting it. Your Ac does a fair job of recirculating and further cooling the air in your passenger compartment but how cold is the air coming from the AC vents at startup when it is processing ambient air?
To test for the capacity of your AC system to produce cold air you could do this.
Close all the AC vents but one, put an air flow meter and a thermometer on that one vent, open all your windows and run the air to the outside of the car.