2013 Audi A6 AC unit

How many what? That's not a term we use in AC repair.

Joules the amount of energy produced by motion or friction. I don't know exactly how a mechanic or auto expert such as yourself would measure this. I am trying to figure out how many units of energy, wether volts or watts or however you would measure it, it takes a cars engine's belt, to run it's AC compressor.

AC consumes 2 different kinds of energy. The compressor is a belt driven pump with an electromagnetic clutch to engage it. It consumes electrical current when it's engaged and also an engine load from the resistance of the pump. It also uses an electrical blower fan and in some cases an electrical condenser cooling fan. You can measure the current draw from the electrical components but you would need a dynomometer to measure the horsepower reduction when the compressor engages.