Maybe, let's see… Your N2 is going to evaporate to a gas, cooling your stuff. The heat moved is going to be the "latent heat of evaporation" which is 199kJ/kg. The gas will be at -195°C with a specific heat around 1kJ/kg, so about 195kJ/kg for to get to 0°C.

Your CO2 is going to sublimate straight from a solid to a gas. The heat moved is going to be "latent heat of sublimation" which is 199kJ/kg. This is only going to be around -78°C and also has a specific heat around 1kJ/kg, so about another 78kJ/kg.

Ok, that seems suspicious, the phase change energies are the same, but it appears to be a total coincidence.

So… if we can hold on to the gas and warm it up before releasing it, then liquid nitrogen wins with about 400kJ/kg compared to 280kJ/kg.

…but depending on our insulation and volume, we may find that we are making a lot more gas than will fit in the cooler so we can't make use of the gas, in which case both choices are about 200kJ/kg.

If you could just keep CO2 from sublimating it would be a huge winner at combined melting and evaporating energy of about 840kJ/kg… but that's why it would rather sublimate.

In the boring category though, water really rocks at 334kJ/kg to melt, so if you supercool your water ice to liquid nitrogen temperatures before leaving you will win.

For safety: Liquid nitrogen needs some special care. If you put your cooler in a small tent, and evaporate off a couple kilograms of liquid nitrogen over night you may not wake up in the warning. The higher nitrogen content of your stuffy little tent will displace oxygen and your body doesn't have a "low oxygen" detector built in. You just die. In contrast, your body does have a "high CO2" detector built in and you would likely have trouble breathing and open the tent flap.

Your analysis doesn't consider that the energy leaking through the walls of the coolbox depends on how cold it is.

That has a pretty significant effect in favour of plain old water.

Are you saying that if I chill my water ice with liquid nitrogren or CO2, that ice will take longer to melt than either of those by themselves?

Yes, but you'll use more than 2kg of LN2 or dry ice for each kg of water ice you chill down to those cryogenic temperatures.

Maybe. The -125C ice could melt faster if it and its container shatters into a billion pieces (a real risk if it’s dropped), massively increasing its surface area.

Thanks!

Was hoping sublimation worked like melting+evaporation, but nowhere close :(

On toxicity, my thinking was you would need a lot more N2 to displace enough atmospheric O2 to cause a problem.

Whereas the sublimating CO2 does displace O2, the CO2 itself is toxic and would probably kill you first. But maybe not in the tent scenario.

Dunno if the DIY N2 has a lot of liquid O2 in it anyway?

CO2 is safer since our bodies have receptors that notice CO2 buildup in the bloodstream, but no receptors that notice lack of oxygen. Breathing pure nitrogen is a very gentle way of killing yourself. You just fall unconscious and die.