LOL ,,, I run a bigger cooler with one Anova 800 watt .
Here's the thing:
It's not really the volume of water that I was worried about.
Assuming you have no food in the cooler, and also assuming that your cooler is well-insulated, the heat loss from the top surface of the water will be the only significant "load" the system will experience.
The surface evaporation (latent heat of vaporization) can be significant, of course, and even without that, you'd have some heat loss simply because that top surface isn't insulated. So people often cover their sous vide containers just to lessen that evaporation and resultant heat loss.
But if we ignore that for a moment, the only thing a larger volume of water does is slow down the rate of rise in temperature of the water (for a given power input). Once the bath is up to temperature, if we assume perfect insulation and no heat loss from the top surface, the heater doesn't need to work at all.
So you could theoretically use a low-power heater for an enormous volume of water if you don't mind waiting a long time for that water to come up to temperature before you start cooking.
But the problem I'm talking about, and what I faced with my Christmas dinner, was that I was going to load 12 pounds of frozen meat into the bath. So the question was:
Will 1200 Watts be enough to maintain the water bath temperature at 131°F accurately for the time immediately after I plunge 12 pounds of frozen beef into that bath?
If this was just 12 pounds of ice cubes, all free and separate, the answer may well have been no! The water temperature would likely go down to near freezing right away, and then need to be brought back up to 131 before I could start timing the cooking.
But of course, the meat has a certain thermal resistance that is going to be much greater than free-floating, and melting ice. And the meat isn't pure water, so its "specific heat" is not going to be the same as that of water. And as the surface of the meat thaws, its thermal transfer characteristics change versus the solidly-frozen meat. And then the thickness of the thawed meat changes throughout the thawing process, etc.
My reasoning was that at the very instant you plunge the frozen steaks into the 131° water, it will behave more or less like pure ice, in the shape of those steaks, with the additional small insulation value of the vacuum packing bags.
I assume that as the outer surfaces of the steaks thaw, the thermal resistance goes up, and the heat load on the bath decreases.
But how fast? And what would the thermal load be initially?
These are far from trivial engineering questions. Do I know the thermal resistance of frozen beef? Do I know the specific heats of both frozen and thawed beef? What calculus would one use to compute the variation in thermal resistance versus time as that particular temperature of water deposits its heat through the bag, and through the ever-growing "thawed shell thickness" of beef and into the frozen inner part?
Beats me!
But the point is: Other than the surface heat loss, it doesn't matter how large your bath is, as long as you are willing to wait for it to come up to temperature.
And this is a simple calculation because we know the volume of water (by measuring the inside dimensions of the cooler).
And we know that 1 BTU is the amount of heat required to raise the temperature of one
pound of water by one degree
Fahrenheit.
And, we look it up, and find that: 1 W = 3.412142 Btu per hour.
So 800 Watts = 2730 BTU per hour. And that's 45.5 BTU per minute.
So your 800 Watt immersion circulator can raise 1 pound of water 45.5 degrees F Per minute.
It's probably easiest to figure your water volume in cubic inches because you've got an inch-graduated tape measure laying around. Measure the width and depth, and then the height to the waterline from the bottom and multiply those three numbers (of inches) and you'll get the volume in cubic inches.
Some Gogle-Fu (or in my case DuckDuckGo-Fu) finds that 1 cubic inch of water has a mass of: 0.0361 pounds.
Multiply your cooler's cubic inches by 0.0361 pounds, and you have the number of pounds of water you'll need to be raising to your cooking temperature.
Now, take the starting temperature of the water and subtract that from the desired cooking temperature, and you can then figure how long your 800 Watt heater will take to get that water up to cooking temperature.
Easy!
But you can see that calculating the heat load created by some bags of frozen steak is an entirely different, and far more complex problem. Far beyond my current knowledge.
This is one of those problems that may be better determined by trial and error with careful measurements.
And I will say that from my research, pork, chicken, beef, etc., all have different thermal resistances, and those thermal resistances are different when the meat is frozen than when it is thawed. Man, this starts to make a guy's head hurt!
Take your cooler, get it up to temperature, and then toss in 12 pounds of ice. Then measure the water temperature at various points in the cooler every five minutes for a while. Let me know what you get.
Now, freeze six sous vide vacuum bags full of water, each weighing 2 pounds, and trying to keep them the shape of a 2" thick steak. Try the experiment again with that and also plot the temperatures every five minutes and see what happens.
Now, try it again with six frozen 2 pound beef steaks in their vacuum bags and plot the temperatures with that "load".
Now, try it again with twelve 1 pound beef steaks (so they're thinner and present more surface area to the bath).
Now try it again, but with chicken.
Try it again with pork.
I'd love to see the temperature versus time graphs for all of those cases.
Now, try all of that again, but with a 1200 Watt circulator.
Again with two 800s and a 1200, and on and on.
I'll bet the results are non-linear with respect to the power because more rapid thawing changes the thickness of the thawed-layer of the meat faster, resulting in some odd curves.
Man, I don't even want to think about it all too hard!
A trip to Target on Christmas eve day and about $80 got me two of the same circulators as you use, and I had my trusty old 1200 Watter, so I blasted it with extreme overkill. To quote Jeremy Clarkson: "More Power!"
But you know what? Your single 800 watt unit may well have worked just as well for me!
The thermal resistance of the meat and bag may well be fairly high such that even with a lot of frozen meat in the bath, the load on the circulator's heater might not be all that much.
I just don't know! But I'd like to know. I really would.
But to make sure Christmas dinner was ready on time, perfectly cooked, and safe. Priceless!
And now I've got the super power sous vide rig at the ready any time I may need it (or be paranoid and just think I need it)!