I get the question quite a bit at www.outsidesupply.com, many people ask about running an air conditioner (AC) on a power inverter. Most people would like to run a window unit for a short period of time to keep something cool when there is no other power source.
My teardrop camper is a perfect example. I do not want to run my air conditioner for 24 hours, I only want to get about 3 to 4 hours of cycled run time. This gives me enough cooling to get in my teardrop camper at a rest stop and get some rest before continuing to drive. I don't do this often but on my trip to the Florida Keys it was great to have this option.
I run a 5000 BTU unit on a True Sine Wave 1500 watt power inverter. I am pretty sure it would work on a modified sine, but I need the true sine wave to recharge some of the batteries I use on the road and also to run a laser printer that I take to print things out of my mobile office.
For what it is worth.
I have this inverter : 
1500 Watt Sine Wave Inverter
I have 250 Ah of AGM batteries installed. This gets me about 3 hours to 5 hours of run time based on how often the compressor needs to kick on in my teardrop. Remember Teardrops are really small campers, so the air conditioner doesn't need to run as much as it would for larger campers.
