DrewE wrote:
Hours; maybe 12ish hours on average, if there is such a thing as average.
This is a question that can be answered pretty well, at least well enough for back-of-the-envelope calculations, by comparing the usable energy storage of the battery with the energy consumption of a residential fridge. According to the Energy Star labels I've seen, a typical not huge fridge use around 1 kWh or a bit more per day on average (under their test conditions). A single marine/RV battery has maybe 50 Ah of usable charge, which multiplied by 12V yields 600 Wh or 0.6 kWh of energy.
Well, except that (a) the usual battery on an RV is rated 75 or 80 AH, so the usable is more like 37.5 or 40 AH, and (b) that rating assumes a 20 hour discharge time, and will be less with a shorter discharge time, so that you are not going to get those 12 hours. Probably more like 8 or 9. Into the bargain, the compressor startup surge (as @oldman pointed out) will likely be beyond the single battery to supply; too many amps drawn at once.