# Archive for August 27th, 2010

### Dry Ice Sublimation Rate

For reasons I’m not at liberty to discuss, we had a cooler of dry ice pellets in the freezer for a few days. I used about a pound of it a time to mumble.

I started with “10 pounds” of dry ice in a half-pound Styrofoam container with 1.5-inch thick walls; the total weights include the container. For what it’s worth, dry ice costs \$3.50/pound under 10 pounds, then \$2.75/pound over that. It used to be plenty cheaper in the old days, evidently, but everything else was, too.

In between withdrawals, the cooler sat in the freezer and and the dry ice quietly sublimated; here’s how the weight varied between uses.

Starting weight: 9.2 lb gross, so I lost quite a bit in transit. Which, as it happened, was about half an hour in a bike trailer during a rather hot afternoon.

A) 7.2 to 6.7 lb -> 0.5 lb / 15 hr = 0.033 lb/hr

B) 3.8 to 3.0 lb -> 0.8 lb / 11 hr = 0.072 lb/hr

C) 2.7 lb to 2.0 lb -> 0.7 lb / 11 hr = 0.064 lb/hr

I’m suspicious of that low number for the first stay, too. Maybe a side effect of having the cooler’s cavity nearly full of dry ice? Or the freezer ran defrost cycles for the other two?

Anyhow, to a back-of-the-envelope resolution the cooler loses a bit over 0.05 lb/hour of dry ice. Call it 15 hr/lb.

The temperature of sublimation is, according to Wikipedia, -109°F. The freezer is around 0°F: a differential of 109°F across 1.5 inches of Styrofoam. Assuming the cooler foam has R=4 with units of (ft^2·hr·°F) / (BTU·in ) and an internal surface area of 304 in^2, the cooler leaks heat at 38 BTU/hr. Call it 11 W.

Cross check: Wikipedia says the enthalpy of sublimation at STP is 571 kJ/kg. Sublimating 0.07 lb = 0.031 kg requires 18 kJ (18 kW·s) and doing that over the course of an hour requires 5 W.

Well, considering the rough-and-ready measurements and the fact that the freezer isn’t at STP and that I’m ignoring gas leakage and a bunch of other stuff, a factor of two error is spot on.

If I were you, though, I’d double-check those calculations before leaping to any particular conclusions. Fair enough?

When all was said and done, I found this thing in the bottom of the cooler. It wasn’t there when we started, soooo

Dry Ice Thing