SJ-Chris wrote:
swag....
Googling, I see that a 13000btu RV AC draws about 13amps at 120v. If your 12v battery is providing this through an inverter, it will be drawing roughly 130amps from the battery. There are also inefficiencies running through your inverter that will probably result in 5-10% more amps needed. So my swag/guesstimate is that your AC will be drawing ~140amps from your battery. Assuming your battery can handle this and that all wiring is adequately sized to reduce voltage drop/etc, it looks like your battery will power your AC for about 1hr 20 minutes. This assumes that your battery was fully charged and you aren't drawing significant power running anything else.
Summary: Not long at all. Use a generator to run your AC
Good luck!
Chris
And I don't know about lithium batteries, but lead acid AH capacity is rated with a 24Hr draw, a 2Hr rating is noticeably less
Couple that with what the max long term current rating is on the lithium battery, it may be less than the current draw of the AC
And then even lithium batteries can't be drawn down to 0 SOC, add that factor in
Then what voltage will the inverter shut down at? may reduce run time even further.
And all this is assuming the inverter can even start the AC