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I'm trying to determine how much dry ice or liquid nitrogen I would need to cool 3300 cubic feet, about 90,000 liters of air, from about 100F (37.78C or 310K) to about 90F (26.67C or 299.81K). I'm assuming that the air is comprised of about 21% oxygen.

How would I go about doing this?

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Do you want to calculate this out of curiousity or actually try it? – Alexander May 29 '12 at 17:34
A phrase to keep in mind if thinking of doing this in practice is "oxygen deficiency hazard". – dmckee May 29 '12 at 18:55
up vote 3 down vote accepted

In the process of cooling the air in the room by vaporizing liquid nitrogen certain amount of heat is transferred from the air to the liquid nitrogen to vaporize it. Then, since vaporized nitrogen will be much colder than the air, further heat transfer continues until the resulting gas mixture achieves thermodynamic equilibrium. Thus, your calculations can be done in three steps:

  1. Take heat of vaporization of liquid nitrogen and its mass to arrive at the amount of heat needed to vaporize it.
  2. Then, take the heat capacity of the air in the room and its mass and find the drop in air temperature that corresponds to the amount of heat (calculated in step 1) required to vaporize the liquid nitrogen.
  3. Finally, use the heat capacities characterizing the resulting gas mixture to find the temperature of the mixture at its new thermodynamic equilibrium.
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It might be useful to list the assumptions under which this holds. This assumes the room is both perfectly insulated and isolated, i.e. no heat transfer through the walls and no air in and out of the room. It also neglects any effect of varying pressure/temperature on physical properties. – Whelp May 29 '12 at 21:47
What temperature value should I use for step 1. STP or the temperature of liquid nitrogen? Also (step 1) "its mass" refers to the mass of one mole? (Links are to quries.) – wizlog Jul 31 '12 at 19:09
You don't use temperature directly in step 1. If you mean to use it to find the heat of vaporization then it'll be the temperature of the substance you're vaporizing, i.e. liquid nitrogen. As for the mass, you use the amount of liquid nitrogen you are vaporizing. In your particular case, this is an unknown variable, so you should leave it as an unknown, continue the calculations to arrive at the formula for the final temperature in the room and ultimately, you solve for the mass of liquid nitrogen. – Adam Zalcman Aug 1 '12 at 14:38

We're not supposed to solve simple problems here, so I can give you directions toward the solution:

First you have to find the mass and the heat capacity of the air in the room to find the heat you need to take away from the air to cool it down. This heat goes into changing liquid nitrogen into gaseous nitrogen: which is consisted by two steps: changing the phase of the matter (latent heat) and then worming it up (heat capacity). Finally, you simply have to equalize those heats to get the mass of the nitrogen.

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