Air conditioning uses huge amounts of power. A large group31 battery trying to power even the smallest window shaker Ac, which is about 450 watts, ccan do it for about 25 to 30 minutes, assuming the battery is still healthy and fully charged.
Even with Ideal high amperage reccharging sources, it cannot be fully recharged in less than 6 hours, and if it does not get fully reccharged nbot only will it not be able to power things for as long ,it actually loses the ability to store electricity. Its capaccity diminishes as if it were a 35 gallon fuel tank which gets smaller each time it is drained, an the ore it is drained and not stretched back to its limit, well kiss that apacity good bye.
Somme ccan and Do run a 450 watt window shaker Ac during the day, completely off of solar, but this requires at least 600 watts of solar and a huge inverter which can handle the start up surge.
The inverter is likely no more than 80% efficient.
So while technically possible to power an air conditioner on battery power and solar, It has to be a huge amount of solar, pretty much more than can fit on a van roof, and a huge battery bank which will not last long unless it is always fully and promptly recharged, and not depleted much more than 505 of its total capacity.
Lead acid batteries come in 3 basic types, Flooded, AGM, and GEL. Lots of people use the latter two terms interchangeably, but an AGm stanbds for absorbed glass matt. the electrolyte is held in the matt. An Actual GEl battery the electrolyte is gelled.
Gel batteries are tempermental in their charging requirements. Too much voltage or amperage and vold will form in the electrolyte instantly reducing capacity forever, however if they are recharged according to their specific needs, makje the best lead acid deep cycle batteries available.
AGM batteries are much easier to care for, but like alllead acid batteries they want to be fully recharged after any significant discharge. They will actually do worse than the cheaper flooded batteries if they are not fully recharged, and if they are recharged too slowly.
Flooded batteries will offgass hydrogen and oxygen when charging in the 80% + charged range. These gases are flammable, and they take some sulfuric acid mist with them. A human should not really be breathing this.
Also, for a house/leisure battery, one really wants a true deep cycle battery, and most every 12v battery which says deep cycle on th sticker, is a freaking liar. They are more dual purpose batteries, closer in construction to a starting battery than a deep cycle battery.
There are a few true deep cycle 12v batteries, but they are pretty big and taller than a regular battery. Such batteries are the GC-15 size group and the trojan T-1275 is an example, though interstate can get them, and these ar emade by US battery. This size group is commonly called a scrubber battery, as in floor scrubber.
ALL other flooded 12v batteries, even if they say deep cycle, are dual purpose batteries that even if ideally recharged and never overdischarged, will only last half as many cycles as a true deep cycle battery.
But 12v marine floodeddual purpose batteries are easily obtained, and warrantyied. Wally world sells a group 29/31 that can give OK service.
AGM batteries can also be great dual purpose batteries and in such duty can give excellent lifespans, if they are recharged properly. There are a few 12v AGM batteries in the regular car jar sizes which can be considered true deep cycle. Lifeline are top dog deep cycle. northstar and Odyssey are very capable duaL purpose batteries. I have an old northstar AGM that has been worked hard, 750 deep cycles over nearly 5 years and is still doing pretty well. but it is a 340$ battery.
The cheaper AGMS are mostly rebranded Deka intimidators. They are not nearly as capacble as the 3 brands listed above, and are rebranded as duracell or energizers depending on region. but they are made in teh USA and are about the same price as the made in China AGM's.
AGMs do not offgass unless severly overcharged and are safe for inside the van charging. It would be difficult to get an AGM to offgass.
Actual Gel batteries are pretty rare, and they will not like the potential high amperage and voltage of the alternator and should not be considered for RV use by 99+%.
Recharging a phone does nto require a dedicated house battery. USB recharging is 5v and usually a max 2.1 amps, this is 10.2 watts. If it takes 10.2 watts for an hour this would be 10.2 watt hours. A group 27 battery contains about 1220 Watt hours, when new and fully charged.
Without the AC, you need ventilation. A fantastic fan exhausting in the roof is the easiest most effective method of exchanging hot inside air for cool outside air. i went the computer fan route instead.
Silverstone FM121, FM181
Noctua IPPC NF-f12 3000 with NA c1 speed controller are my favorite fans.
The fm181 is about 7 inches in diameter and draws about 3.5 watts on high speed, and moves 165 cubic feet of air per minute.
With just Phone recharging and fans, you do not even require a house battery. CArry one of these jumper boxes. Keep it fully charged always, for when your engine battery refuses to start the engine and you can jumpstart yourself.
I would recommend NOT using these jumperpacks to power the phones or fans, although they can. These do not have a lot of capacity, despite their ability to help a depleted engine battery start the engine.
YOur existing engine starting battery, is not going to last long when used as a deep cycle battery. When it fails, replace it with the largest marine/dual purpose battery which will fit, and if you want some extra insurance, get one of the high$$ AGMS from Northstar or Odyssey, as these have so much CCAm that even depeted 85% of their total capacity they can likely still start the engine, where a regular marine battery could not if discharged 85% of its capacity.
Another issue with Newb's is they assume the alternator is a free magical near instant battery recharger. The reality is, that while an alternator is capable of delivering high amperage to a depleted battery, the alternator is controlled by a voltage regulator. Voltage is electrical pressure. Long story short is the voltage regulators are not concerned with promptly returning a depleted battery to full, they are programmed to return a slightly discharge battery to its starting point and to NOT overcharge it. Soon after starting the voltage will drop from the mid 14 range to the mid 13 range, and the amperage the battery will accept at 13.7 is only 1/3 of that as it would at 14.7v.
And even at 14.7v, it takes the healthy group 27 battery no less than 45 minutes, with a thick copper circuit in between the cold fast spinning alternator and the depleted battery, to get the battery to 80% charged, and no les sthan 3.5 hours to get from 80% to 100% charged.
And 100% charged is the single most important thing regarding lead acid batteries that are recularly cycled, they must be returned to 100% as often as possible as soon as possible, or they simply ned to be replaced at much shorter intervals, and once the original warranty is covered, you get to pay full price for the next battery.
A plug in charging source is very wise for when one can plug in. Most of the garage 'smart' chargers are pretty much junk though as they too give up prematurely on the voltage held, and while they will say the battery is fully charged, it is not, and even if left plugged in for another day, might not fully charge it.
There is a lot to learn when living on battery power, and it can be taken to extremes. A newb needs to know that the lead acid battery always wants to be 100% fully charged, and kept cool. They need to know that regular household electrical appliances like coffee makers, hair driers, air conditioners use obscene amounts of electricity, and are very impractical to try and power these from battery power alone.
Refrigeration is a pretty big hurdle too. replacing block ice every 5 days gets annoying and expensive.
A household dorm fridge on an inverter uses twice as much electricity as a 12v compressor refrigerator, but the 12v refrigerator is obscenely expensive, ~ 500$ for 1.8 cubic feet.
The 1.8 cubic foot chest type of 12v fridge can, in a sunny environment, get away with 60 to 80 watts of solar.
More solar is always better though as cloudy days are inevitable.
I have 198 watts on my roof, and power my front loader fridge, the laptop several hours each night and morning, and can turn my van into a wind tunnel. With my windows covered to block sun, I can keep the interior as cool or cooler than ambient temps. All my lighting is LED on dimmers, and i usually only have issues with not enough charging source via solar or alternator in mid winter with short days and longer nights.
Likewise electric space heaters are a no go on battery power. If I plug into the grid, 200 watts will keep my lightly insulated van in the mid 50s when outside is mid to high 30's. I could run this heater on my inverter for ~ 3 hours before the fully charged group 27 battery is in the 50% range. if I fell asleep with the heater on My fridge would shut off well before morning.
So read the above more than once, and ask some more questions and i can better establish what you need to power what you can and cannot live without.