The thermal output (heat amount per time unit) transferred through a wall, L thick, equals
where: λй is the conductivity of the material wall, S is the section area of the wall through which the heat is transferred, Tout and Tin the temperature outside and inside, correspondingly.
Let us have a cubic box with an internal size of а х а х а = 20х20х20 cm, and the walls, L thick. Then the average section area of all 6 walls (planes) will be:
During the t time, the heat amount Q passing through the walls, will be:
This heat will evaporate our thermal accumulator (dry ice or liquid nitrogen) of m mass. To evaporate this mass amount, we need to spend the quantity of heat Q1 equal to
where: Hq is the so-called latent heat of evaporation (of boiling, sublimation, condensation, etc.).
As long as the heat accumulator has not evaporated, the inside temperature is kept at its evaporation level. All the incoming heat is used only for evaporation since the generated gas should go out through a valve. Let us assume that it has no time to get heated before exiting the box. In this case, Q=Q1. Therefore, we can calculate the mass (m) using the following equation:
Let’s have a look at hard numbers:
Heat conductivity of some thermal insolation material:
| material | λй, W/m*К |
|---|---|
| foam plastic | 0.07-0.1 |
| fiberglass | 0.03-0.05 |
| air | 0.029 |
| aerogel | 0.015-0.020 |
Temperature and evaporation heat at atmospheric pressure:
| substance | Tevap, оС | Hq, J/g |
|---|---|---|
| CO2 | -78 | 586 |
| N2 | -196 | 198 |
Dry ice is much better than liquid nitrogen.
t = 700 hours
Let’s take fiberglass as a heat insulator, a wall, 10 cm thick, and an outside air temperature of +5 оС
Then we’ll need about 57 kg of dry ice. For comparison, there’s room in the box for a little more than 12 kg of dry ice.
Other words to keep the temperature of -78C for 700 hours in the box of 20x20x20 (8x8x8″)you need a box with dry ice of 40x40x40 cm (16x16x16”)
To keep the temperature of -20C for 700 hours in the box of 20x20x20 (8x8x8″)you need a box with dry ice of 25x25x25 cm (10x10x10”)
To keep the temperature of +5C for 700 hours in the box of 20x20x20 (8x8x8″)you need a box with dry ice of 20x20x20 (8x8x8″)