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Boiling is the process by which liquids are heated beyond their "boiling point" and undergoes the change from the liquid phase to the gaseous phase. Boiling is the converse process of condensation, in which an element or molecule in it's gaseous phase is converted to a liquid.
An element or compound will boil after passing its respective boiling point, but there are more aspects to this process than just temperature. The system must be open to the atmosphere. If the system is completely enclosed, the liquid will reach its critical point. After a liquid has been heated past it's boiling point, the molecules will start to behave differently than in the liquid phase. They will take on a less organized structure, and the molecules will begin to enter the atmosphere in the form of a gas.
At the boiling point, the liquid begins its transition to the gaseous phase, and will actually hold its temperature at this point. For example, when water reaches 100 degrees centigrade, it will begin to boil to its vapor phase and the liquid that has yet to boil will hold at the constant 100 degrees. The water will be unable to change temperature until it has completely shifted from the liquid phase to the gaseous phase. The distinction in this case must also be made between boiling and evaporation. Evaporation is a similar process in which the liquid continuously changes to the gaseous phase, though it is a process that usually occurs at equilibrium, and at nowhere near the rate of boiling. More information can be found at enthalpy of vaporization.
The temperature at which a liquid will begin its transformation into a gas is dependent upon the pressure it is under. For instance, water boils at 100 degrees centigrade under a pressure of 1 atmosphere. If the pressure is lowered, the boiling point is actually lowered. This also means that an increase in pressure will increase the boiling point of the liquid. Since pressure can also be related to altitude, the farther away from sea level a system is, the lower the boiling point will be for any liquid within said system. This is to say that the boiling point of water is 100 degrees in San Francisco, while it will be a couple of degrees lower at Lake Tahoe where the altitude is significantly greater and as such, has less pressure on the system.
Water has been an excellent example so far, but in actuality isn't the best example for a wide array of liquid to gas transitions. For example, Nitrogen is a gas at room temperature and is most prevalent on Earth in this phase. This is because Nitrogen has a boiling point of roughly -196 degrees C. Only at temperatures below this will Nitrogen be found in it's liquid phase, and during its transition will keep the constant temperature as it changes phases. This property of keeping its temperature as a whole until all of the liquid has finished boiling allows it to be used in industrial properties as well as in some small scale home use.
Say you find yourself with some cream, sugar, vanilla flavoring, an industrial sized vat, and a hunger for ice cream all in your home. However, you don't have the ice or salt to help you in your task to make said ice cream. You remember reading this wiki, and the bit about liquid nitrogen, and run down to the local chemical supply store and pick up a small amount of liquid Nitrogen.
After obtaining all of these ingredients, you are ready to make the ice cream. Just combine the 3 main ingredients in your vat, grab a large wooden spoon to stir, and slowly start adding the liquid Nitrogen. Make sure to constantly stir, and add the Nitrogen slowly. In under five minutes you should have some completely edible ice cream. Make sure protective gear is worn at all times. This whole process is possible because the Nitrogen remains at -196 degrees during the entire time that it is boiling, and will reduce the temperature of it's surroundings, which in this case was the ice cream ingredients. Other elements normally in the gas phase at room temperature will have similar properties.
In quick summary, note that all of the elements found in the gaseous phase at standard temperature and pressure, will have a boiling point much less than 0 degrees centigrade.