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I took this picture from wikipedia. As you can see the higher pressure the higher temperature.

enter image description here

However, As I read the article from this site they said that,

At higher temperatures, the molecules move quickly and spread out. This means that there are fewer molecules in an area. Fewer molecules result in lower air pressure

which conflict with the graph. It makes me confused a lot could you explain to me how does it work??.

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  • $\begingroup$ While I can understand some of what they are intending, personally I find that quoted section wrong. It seems to imply that higher temperature is causing lower pressure directly. It doesn't. They're trying to condense a very complex system into a single cause. $\endgroup$
    – BowlOfRed
    Commented Apr 20, 2023 at 20:40

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The confusion arises from comparing two different scenarios. When considering the relationship between atmospheric pressure and temperature, we're typically looking at a situation where the air is free to expand or contract. In contrast, the ideal gas law (PV = nRT) applies to situations in which the volume and the number of moles are held constant.

Atmospheric pressure and temperature: At higher altitudes, the temperature is generally lower, and the air pressure is also lower. In this scenario, the air is not confined and can freely expand or contract. When the temperature increases, the air molecules gain kinetic energy and move more quickly. As a result, they spread out, and the density of the air decreases. Since air pressure is proportional to the density of the air, a decrease in density results in a decrease in air pressure.

Ideal gas law (PV = nRT): In the case of the ideal gas law, when the volume (V) and the number of moles (n) are held constant, an increase in temperature (T) will result in an increase in pressure (P). This relationship can be observed in a closed container, where the gas cannot expand or contract freely. When the temperature increases, the kinetic energy of the gas molecules increases, causing them to collide with the container walls more frequently and with greater force. This results in an increase in pressure.

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  • $\begingroup$ Omg, It is very clear I'm fully understand now Thanks a lot $\endgroup$
    – Patrick
    Commented Apr 20, 2023 at 20:02
  • $\begingroup$ How do you know that density decreases more than temperature increasing such that density multiplied by temperature decreases? $\endgroup$ Commented Apr 20, 2023 at 20:05
  • $\begingroup$ @naturallyInconsistent The statement in the link provided is an oversimplification. The relationship between pressure, density, and temperature (P/ρ = RT/M where n is constant) is more complex than just assuming that density decreases more than temperature increases. In reality, the relationship depends on the specific conditions, such as the type of gas, its molar mass, and the changes in pressure and volume. In some cases, an increase in temperature could cause a decrease in density that is greater than the temperature increase, while in other cases, it might not. $\endgroup$
    – tesla
    Commented Apr 20, 2023 at 20:11
  • $\begingroup$ I think we can appeal to constant entropy (isentropic = adiabatic). Then $T^{3/2} (V/N) = $ const, and now if T increases, volume per particle decreases, density increases. Thus it should be false. Something is really weird here. $\endgroup$ Commented Apr 20, 2023 at 20:21

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