Buttoni
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You can use a car battery with an inverter for your CPAP. We have done it many times. We have two solar panels on our garage roof hooked up to keep 3 batteries charged.
It is a pain to run willy nilly in an outdoor kitchen. I do the food prep (cutting, organizing) indoors, and haul it outside in a wheeled ice chest. If I'm doing dutch oven, I run four at a time with four different recipes. It's just easier. We have a covered patio outside our milkhouse I have a kitchen set up at. And a water hydrant real near by. We don't have an inground firepit, but I have a portable one that can be moved closer if I'm cooking stir fry.
I'll tell my husband about the CPAP battery option, but we don't have a solar set up yet. My husband is not too adept with such things. He's been reading some on it, but hasn't done it yet. Sounds like YOU'RE pretty set up for smooth cooking there. I like your wheeled ice chest idea. Must remember that.