How to Calculate the Change in Freezing Point with Altitude
Water boils and freezes at different temperatures depending on the altitude. You can find the boiling and freezing points of water at any given altitude.
As you learn in school, water freezes at 32-degrees Fahrenheit and boils at 212-degrees Fahrenheit, but this is not always the case. The boiling point and freezing point of a liquid will change depending on altitude. This makes a significant difference in cooking and baking. At higher altitudes, cooking takes longer, doughs rise faster and foods dry out more quickly. Often, recipes include “high altitude” instructions. If not, it can be helpful to know what the freezing and boiling point is at your altitude.
Things You Will Need
- Graphing Calculator
- Barometer (optional)
The reason that freezing and boiling points change based on altitude is the resulting change in air pressure. For instance, in Denver, the Mile High City, a liquid boils at about 202-degrees Fahrenheit because of the lower air pressure at its higher altitude. A liquid boils when the pressure of its vapor equals the pressure of the atmosphere, but at a higher altitude, there is less atmospheric pressure on the liquid. In Denver, for instance, there is an atmospheric pressure of 12 pounds-per-square-inch while in Los Angeles, the air pressure is 14.7 pounds-per-square-inch.
The change in freezing point at different altitudes is much smaller than the change in the boiling point. The freezing point increases very slightly at higher altitudes, due to the air pressure. Because ice takes up more space than water, a lower air pressure will cause water to freeze at a slightly higher temperature.
To find the altitude of your location, you can use an atlas or an internet search to find the altitude measured in feet.
You need to calculate the air pressure in inches of mercury. The formula to find the air pressure from the altitude is as follows:
pressure = 29.921 * (1 - 0.0000068753 * altitude)^ 5.2559
Alternately, you can use a barometer to calculate the air pressure and then convert the units. 1 Bar=29.53 inches of mercury.
Once you know the pressure, you can calculate the boiling point with the following formula. You may need to use a graphing calculator for this since it is a logarithmic equation.
boiling point = 49.161 * ln(pressure) + 44.932
This will give you the boiling point of water in degrees Fahrenheit.
The freezing point of water will be about 32-degrees Fahrenheit on every surface on Earth, whether you are below sea level or on Mount Everest. Even if you multiplied the air pressure at sea level by 131, you would only lower the melting point to 30.2 degrees. And that assumes an atmosphere that weighs nearly 2 tons. On the other hand, if you reduce the air pressure to 3/500ths of the pressure at sea level, the freezing point is only 32.018. This is the triple point, meaning that at any pressure below that point, water will never be liquid, only solid or gas. It will be 32-degrees Fahrenheit. If you are free-floating in a pure vacuum or hanging out in a black hole, check a water phase diagram.
Learn How Boiling Points Work
Learn How Freezing Points Work
Find the Altitude of Your Location
Calculate the Air Pressure of Your Location
Find the Boiling Point of Water at Your Location
Find the Freezing Point of Water at Your Location
If you don't have a graphing calculator, there are several online calculators for finding the boiling point of water.
Jaime is a writer living in New York City.
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