|MadSci Network: Chemistry|
Water, or anything for that matter, boils when the the vapor pressure of the liquid in question equals the ambient pressure. There is a simple equation that gives you the vapor pressure of pure water at any temperature. Just look it up in the CRC.
In regard to your question, the ambient pressure is usually the pressure of the atmosphere at a particular elevation. Since pressure decreases with increased altitude, in the mountains, the vapor pressure of water reaches ambient pressure at a lower ambient pressure than it would at sea level. Therefore, water boils at a lower temperature in the mountains and you have to cook your pasta longer to get it just right.
Now, if the container in which the water was boiling was closed, such as a pressure cooker, the ambient pressure changes as the water temperature increases. This is because of two reasons. First, the ideal gas law you mentioned. But also, the released water vapor significantly changes the ambient pressure (Usually, this is negligible because the released water vapor is so small compared to the entire atmosphere). So you have the pressure of the heated water vapor, the initial pressure of the air inside the pressure cooker, plus the increased pressure due to the increased temperature. Since the ambient pressure is greater, the water will boil at a higher temperature. The extent of this depends on the size of your container. When the container is really big, the size of the atmosphere for example, it doesn't make a different. But for small containers, such as a pressure cooker, the water will boil at a much higher temperature. Another question is, will the water ever boil? I leave that to you. If so, or not, what conditions will govern the behavior?
The above discussion about closed containers assumes that the container is perfectly sealed, which allows the pressure in the airspace above the liquid to build up. Most pots do not have perfectly sealed lids. They allow both steam and air to escape which keeps the pressure down. If you want your water to boil faster, I suggest you put the lid on because it insulates the contents allowing them to heat up faster to the boiling point. Remember the saying - "a watched pot never boils".
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