What is the relationship between air temperature and air pressure?

The pressure and temperature of any gas, including air, are directly proportional, according to Gay-Lussac's law. This gas law shows that, if the mass and volume of any given sample of gas are held constant, as the sample's temperature increases, so too will its pressure, and vice versa. This is because greater temperature causes the molecules of gas to have greater kinetic energy, which results in an increased number of collisions with the walls of their container, increasing pressure.

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Pressure and temperature are related to each other by Gay-Lussac's Law.  This law says that P1T1=P2T2, or the initial pressure multiplied by the initial temperature is equal to the product of the final temperature and the final pressure.  Pressure and temperature have an inverse relationship.  In other words, increasing one, will cause the other to decrease. 

So if you increase the air temperature, the pressure is going to decrease.  If you decrease the air temperature the pressure is going to increase.

 

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The relationship between the two is that air temperature changes the air pressure. For example, as the air warms up the molecules in the air become more active and they use up more individual space even though there is the same number of molecules. This causes an increase in the air pressure.

The same goes for cooler air. When the temperature cools, the molecules slow down and they do not move and bump into each other. This causes a decrease in air pressure.

An easy way to understand this concept is by comparing car tires in the winter and car tires in the summer. In the summer the air is a lot warmer so the molecules are moving around a lot. The tire expands and you not need as much air because the pressure in the tires is high enough. In the winter, when the air is cold, the molecules are moving very slowly. Many people need to add more air to their tires because there is not enough pressure.

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As temperature rises, so too does pressure.  As pressure rises, temperature rises along with it.  Obviously the opposite is also true if they are decreasing.

One great example of this occurs if you happen to use a propane tank (particularly the small ones) while cooking at a campout or picnic.  As the gas inside the tank is burned and the pressure falls, you will very often see frost form on the outside of the bottle if it isn't too hot out.  As the pressure inside has fallen precipitously, so too will the temperature on the outside of the bottle, leaving you with the frost.

Check out Gay-Lussac's law about the direct relationship of temperature and pressure.

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