If you leave a car continuously running, how large an inverter can be placed on it to make electricity?

I am trying to find a cheap back-up option for portable batteries that are solar charged. Could a car with a 2L engine run a 4000w or 5000w inverter to give 240V electrical power?
Update: I want to power a food kitchen in a caravan for 4-6 hours a day in summer at the beach. Later I would like to have enough solar panels and deep cycle batteries to do it mainly by solar, but want a cheap start-up option, and a back-up later on. Would a car be as fefficient than a generator if excess power was... show more I want to power a food kitchen in a caravan for 4-6 hours a day in summer at the beach. Later I would like to have enough solar panels and deep cycle batteries to do it mainly by solar, but want a cheap start-up option, and a back-up later on. Would a car be as fefficient than a generator if excess power was stored in a few deep cycle batteries.
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