How can a solid turn into a gas without going through the process of evaporation?

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Sublimation is the process of a substance changing from a solid directly to a gas without going through a liquid phase first. Carbon dioxide undergoes sublimation at normal pressure and temperatures above  -78.5 degrees Celsius. Solid carbon dioxide is called dry ice. 

Evaporation is the transition from liquid to gas at a temperature below the substance's boiling point. Evaporation isn't a step in sublimation because substances that sublimate have no liquid phase at atmospheric pressure.

Sublimation only occurs at a pressure  and temperature below the triple point in a substance's phase diagram. Carbon dioxide's triple point occurs at a very high pressure. (The triple point is the temperature and pressure at which a substance will exist as a solid, liquid and gas all in equilibrium with each other.) Carbon dioxide would need to reach a pressure of about 5.1 atm to be in a liquid phase. 

Iodine is another substance that sublimates at normal pressure. It's a silvery-colored solid that forms a purple gas.

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