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You won't run it for very long on a battery. Typically coolboxes of this type draw up to 7 amps on 12v. Working on my usual rule-of-thumb you can get 50% of the stated capacity of a battery, so a 110Ah large leisure battery will give 55Ah. Divide that by 7A and you'll only get 8 hours running!
Even a small coolbox drawing 4A would only run for 13 hours or so.
Have a look at...
www.glenp.org.uk/batteriesfaq.html
I'm still working on these FAQs but it might help a bit to explain.
Glen
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