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Modeling Scenario

1-012-Sublimation-Modeling Scenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: sublimation dry ice

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Resource Image We offer data on the sublimation of dry ice (carbon dioxide) collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the differential equati


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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Course Level
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level


Matter exists in several states: plasma, gas, liquid, and solid. When a solid becomes liquid the object melts. When a liquid becomes a gas the object vaporizes. When a solid becomes gas directly the object sublimates. A readily available example of sublimation occurs when the solid, dry ice (solid carbon dioxide - CO2), becomes gaseous.

Now if we had a solid block of dry ice we would notice it ``disappear'' as it sublimates into its gaseous state. Indeed, the mass of the block of dry ice would decrease. A reasonable question to ask is, ``At what rate does the mass decrease as the dry ice sublimates?" A related question is, ``What does the rate of change of the mass depend upon?''

Some years ago in a course we were teaching we too wondered whether we could model the sublimation of a piece of carbon dioxide. At the time (over 30 years ago) dry ice was used to pack ice cream shipments. One day, because we had received some things in a shipment containing dry ice, we thought of collecting data on the sublimation of dry ice. While we had colleagues who were true engineers and scientists on our teaching team, we decided, as a mathematician who was pretty much an inept lab fellow, to go this one alone.

We set up a modest device consisting of a tray, in which we placed our dry ice on a scale which could render mass in grams to the thousandth of a gram. We zeroed out the scale (i.e. we noted the mass of the tray and then noted the mass with the initial dry ice amount on it so that we could tell from total mass data exactly what our dry ice mass was as time progressed) and began to collect data. We should say we really lived dangerously, for we did this all for the first time in class with two students in the first row recording the mass every 30 sec. We have since lost that data, but there was a very unexpected thing that happened. The mass of the dry ice, rather we should say the mass of the zeroed dry ice and tray, went up(!) in the first few minutes. We continued to collect data on that run and we all went home to ponder what was going on. I had the advantage of holding the equipment and some more dry ice. After class I tried the experiment again and found the problem. The dry ice was so cold, below sublimation temperature of dry ice, -78.5$^{o}$ C, that it was causing water to condense on the tray, and upon inspection, I could see the ice film on the tray. That was why the mass went up on this configuration for a while.

Article Files


Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations



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