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I would like build a package with frozen food products (to -18 °C). The products are small balls of pizza dough (diameter of 4 cm). Total dough ball weight is 10 kg (333 balls, 30 grams each).

I'm going to put them into a styrofoam package with dry ice (sealed and insulated) that has inner dimensions 33 x 23 x 28 cm and a wall thickness of 3.5 cm. The dough balls will be stored from 2 to 5 days.

The data for the dry ice:

  • 16 mm granules
  • Sublimation temperature: -78.5 °C
  • Density: 1.1 - 1.4 g / cm^3

External temperature where the box is stored:
a) 10 °C.
b) 21 °C.

My question:

How much dry ice should I include to have all balls still frozen, i.e. have them in a temp. around -2°C, in the case when:

a) time of storage = 3 days
b) time of storage = 5 days

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  • I assume you're fine with a practical answer based on people's experience, rather than some kind of theoretical physical calculation? (You provided a lot of detail, and I'm not sure if that's just you being helpful (yay) or if it's because you want that kind of detail in an answer.)
    – Cascabel ♦
    Oct 21, 2014 at 18:27
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    This is going to depend on the details of the packaging -- how thick the foam is, how well the lid is sealed (though some provision must be made for escaping CO2), what other insulation is around it, what surrounding conditions will be... (A good cooler can keep foods frozen for three days at summer temperatures just with normal ice, if everything starts frozen/prechilled and there is minimal air gap. A bad one under the same conditions would be doing well to last a day.)
    – keshlam
    Oct 22, 2014 at 0:34
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    This looks like a homework question. In any event, this style of question seems more natural in the physics or engineering section than here. It is borderline science of cooking but definitely not food-science.
    – user110084
    May 16, 2017 at 17:18

1 Answer 1

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Everything inside the sealed box will reach an equilibrium temperature of -78.5C for as long as there is dry ice inside. You are still missing a few assumptions such as the conductivity of the box (typically 3.3x10-3 W/m/K) and the heat capacity of your dough (assumed to be same as ice).

Once everything has reached that temperature, just to overcome "cold losses", at 10C outside, you need between 1.8 and 2.3 kg for 3 days and between 2.9 and 3.7g for 5 days. At 21C, between 1.9 and 2.5 kg at 10C, 3.3 and 4.2 kg at 21C. You will need an additional amount to chill all the contents (air included) down from -18C to -78.5C, which comes to at least 2.2 kg.

All of this is based on a simplified model and is likely an underestimate.

One problem as @keshlam pointed out is the sublimated dry ice in a sealed container and the pressure build up. Also, between 18% and 28% of your box will be filled with dry ice. 10kg of dough as a single lump will take up another 5% of your cavity, before you consider packing efficiency of spheres. All that leaves you with not a lot of room for gas expansion.

Without any dry ice, if everything is chilled to -18C first, your sealed box should just about keep the dough balls frozen for 3 days at 10C outside.

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