Whilst the question was about recharging batteries, no suggestions were made regarding USEAGE
of fridges and specifying between the different types of fridges available on the market today.
I notice the poster did not advise what type of fridge was being refered to, we all assumed it was a 12 volt compressor fridge.
So let's clear the air somewhat.
There are mainly TWO types of fridges available for our useage today.
The first is the THREE WAY FRIDGE, which utilises chlorine gas under pressure. The gas is super pressurised by heat, this heat is generated by either a gas flame, a heating coil of resistance wire powered by 12 volt, or another such wire powered by 240 volt.
As the 12 volt operation relies upon a resistance wire, these fridges have a tendency to be POWER HUNGRY when operated on 12 volt, therefore NOT recommended for such operation.
Alternatively, when operated on LPG these fridges are silent and can run for two weeks at a time on a 4.5 kilo bottle of gas pending on your temperature setting.
Down side of gas operation, is loss of efficiency in tropical areas. However, for the home handy man/woman, this can be dealt with by affixing Computer fans to the rear coils with a speed control thus allowing faster air transfer over the coil thereby negating the effects of tropical climes.
The 12 volt compressor fridges operate differently. They are fitted with a 12 volt compressor which runs from a 12 volt supply, being from car, deep cycle battery or power supply from 240 volt mains.
The trick with either of these fridges is to fully stock them 24 hrs before you depart, allowing the internal temperatures to come down to set levels thereby reducing the load on the compressor and the demand made on the power supply once you get under way. Keep them in a cool place and ensure there is sufficient air flow around them when transporting in your vehicle, air flow is very important, as it transfers the heat away from your foodstuffs. Reduce the airflow and your fridge becomes less efficient.
If you've chosen a threeway fridge, it's really no big deal to operate successfully. Stock it as above and plug it into 240 volt 24 hrs before departure, believe me, it will cool things down pretty efficiently in that time. Place fridge in car ensuring adequate airflow and plug in 12 volt source.
IMPORTANT, many cars today, DO NOT HAVE ADEQUATE wiring to cater for the loads such fridges may require from time to time, therefore ensure from your friendly auto electrician, yours IS adequate.
In our case, I've had a relay installed, so as long as the engine is running, so is the fridge, turn engine off, and fridge is off too. This is to ensure the fridge doesn't flatten your battery.
I've found that three way frdiges running on 12 volts work perfectly fine in this manner.
Arriving at campsite, fridge is removed from vehicle and connected to LPG and remains connected for entire camp operating faultlessly and silently.
Compressor fridges require 24 hour cool down same as 3 way's do, then place in car and connect to 12 volts, requirements for air flow and electricity supply, are same for these fridges as for 3 way wiring.
Once you arrive at camp site, remove fridge from car and connect to your CHOICE of 12 volt power.
As many posts here have already demonstrated, there is an abundant choice of what that could be, however which ever choice you choose, ONE of them most certainly will be a battery.
I would advise such a battery be of the largest capacity you can afford in AMP HOURS, said battery MUST be FULLY charged before leaving home and of course your fridge temp is also at it's required setting.
Provided this is the case, and battery capacity is of robust standard, with reasonable useage, I'd expect the battery to last for at least 36 hours, provided no new warm foodstuffs find their way into fridge.
Now, if you've connected a solar panel to such a set up from the moment you've placed it from the vehicle on the ground, and the capacity of panel is at least 80 watts, I see no reason for it not being able to keep the battery capacity at acceptable levels for the time you are at that camp.
WORD OF WARNING HERE;
Fridge sellers do not warn purchasers of the risk of FIRE, from overheated wiring, especially if fridge leads are allowed to double up on themsleves in vehicles and have objects placed upon them.
NEVER allow them to tangle or double up on themselves, and never place objects particularly flammable objects on top of them as they get hot, and there are cases on record, where vehicles have been lost as a direct result from such fires.
For my money, and simplicity's sake, I recokon the three way lpg fridges are tops. All you need is a lpg bottle and your away.