What size of the solar panel do I need for an air conditioned system (24,000 BTU)?

I'm guessing that if you have a reasonably efficient AC unit, it will draw about 9.5A at 240Vac. If that's the case, then you'd need your PV system to put out at least as much while the AC unit is running: About 2280W. If you run the AC for 24 hours per day then you would use about 54kWh of energy. To offset that with solar, if you are in Central California and have an average of 5.5 hours of full sunlight - you would need roughly 10kW of PV on your roof.