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Unfortunately, the specs of the appliances will only provide the maximum power consumed, not the average. For instance, a residential refrigerator with a compressor will consume much more power when the compressor kicks on.
To get an accurate idea of your energy requirements, you need to determine the long term load. Consider a load tester, such as a "Kill A Watt" brand tester. You can buy one of those for about $20.
A tester for that price will only handle up to 20A @ 120VAC, but it has a standard outlet, so you can plug it into your RV (with adapter) or individual appliance - and test one appliance at a time (to stay under the limits of the meter). The Kill A Watt will tell your average power consumption over time - which is more accurate than reading the specs.
You will then need to figure out the AH draw (Amp-Hour, or Amps x Hours) at 12VDC. This gets complicated as you have to determine power factor and losses at the inverter. But a good rule of thumb is to subtract say 10~20% for these losses.
For example, say your device you are testing takes maybe 100Watts at 120VAC.
Then simply use OHMs Law (ignoring things like the Power Factor of AC for now), and by dividing the 100Watt figure by 120V, you get an answer of about 1Amp. Then multiply that by 10 - to get to 12V of your batteries.
The answer then is the device drawing 100W at 120V is equivalent to around 10Amps at 12V.
Now, add 10 or 20% to that figure as a fudge factor to account for the AC power factor and any inefficiencies of the inverter.
So you will end up with say 12Amps. This is the approximate current demand of the item at 12V.
So, if you have a battery rated at 80AH, that means it will supply 80A for 1Hour or 1A for 80Hours (but we need to do something with Peukert's Law).
Therefore, if you put a 12A load on the batteries, you should get almost 7 hours of run time.
But... Peukert's Law states that you cannot get full capacity out of the battery at high discharge rates, so you may need to subtract another 10% or so from the run time. Peukert's Law is specific battery brand and model dependent, and Trojan batteries are generally the most favorable in that regard.
OK, so now we are at 6hours run time for an 80AH battery supplying 100W @ 120VAC through an inverter.
But we are not done yet.
You will severely shorten the life of your deep-cycle house batteries if you drain them completely. The rule of thumb for longest life is to never discharge them more than 50% capacity.
Uh oh... that now means you have to reduce the time by 50%.
Final answer - 3 hours run time.
Of course this is hypothetical, but you can see the complexity of the issue.
Also, consider some power reduction items, such as replacing all of your 12V incandescent lighting with LEDs. LEDs consume about 1/10th of the energy that incandescent bulbs do.
And a couple of solar panels will help to recharge your batteries. You won't be able to keep the charge up on your batteries if you run the A/C, but RV refrigerators (the kind without a compressor) are pretty efficient, and three or four 150Watt solar panels just might supply enough power to keep the batteries above the 50% discharge point.
Needless to say, it gets complicated.
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