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Graham,
I think you'll need a bit more than a 7Ah battery to give acceptable results.
Check the current required for the stuff you want to power and then double that number as a "Ah" target.
(This infers a 7Ah would power 3.5A for one hour before getting too low)
I use a couple of 20Ah gel cell golf buggy batteries - but don't use dew heaters....
Others have gone for large and heavy maritime boat/ caravan batteries - 120 Ah etc.
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