I'm doing some calculations for shipping frozen items and something's confusing me. It seems that salted ice outperforms dry ice, so why would anyone ever ship using dry ice? Dry ice is a lot more trouble and more expensive too, right? Btw in case you're wondering about gel packs & other special packs, they are just gelled water. Regardless of wild claims they are exactly the same as ice packs in terms of performance. The advantage is they leak slower. So when I talk about ice packs I am talking about gel packs & etc. too.
Dry ice is far colder and has a higher heat of vaporization (/fusion) than water ice. But this first advantage is actually a disadvantage. The colder the shipping package is, the faster it absorbs heat. Heat transfer is directly proportional to ΔT. At -78.5C it's so extremely cold that heat absorption is 3-5 times faster than a package shipped with ice packs. Its heat of vaporization is only 70% higher. So the higher heat absorption easily trumps this. So the dry ice thaws much faster than water ice. Then once all the dry ice is gone the frozen food rapidly climbs to freezing temperature and thaws normally. Meanwhile the food with salted ice packs is still fully frozen. Because the amount of energy to raise the temperature once the dry ice/water ice thaws is much less than the energy it takes to thaw.
Normally you only ship fresh food with ice packs, not frozen food. Because ice packs have a freezing point of 0 C. And food has a freezing point of about -1 to -4 C. So the frozen food thaws before the ice packs even start to thaw, the ice pack's big heat of fusion is totally useless, and they do little to keep food frozen. That's why the freezing point of your ice packs should be lower than your frozen item; so that the packs melt first not the frozen item. So then comes in dry ice with its -78.5 C freezing point and the food stays completely frozen until all the dry ice is gone. It does a much better job than normal ice packs at keeping frozen things frozen. But you can also get salted ice packs with freezing points of -5C or lower. Why didn't they do this instead? It's not as cold initially, but I think it stays cold longer. Or did I miscalculate something?
Am I missing something? Or should every shipper ditch dry ice and switch to salted ice?
A few figures in case you want to play with the numbers:
Specific Heat of Water 4184 J/(kg˚C)
Specific Heat of Ice 2108 J/(kg˚C)
Latent Heat of Fusion for Ice 335000 J/kg
Dry ice Latent Heat of Vaporization 571000 J/kg
Dry ice Freezing Temperature -78.5 ˚C
Specific Heat of Dry Ice 700 J/(kg˚C)
Specific Heat of Carbon Dioxide 800ish... but effectively zero because it gets vented out of the package.
Styrofoam Thermal Conductivity 0.03 W/(m K)