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From the ideal gas law, we are aware that PV = nRT, which seems to suggest a direct relationship between pressure and temperature, or that as temperature increases, pressure increases.

In my geography book, however, it is written that "The equator receives direct rays of the Sun, this causes the temperature to rise, hence causing an equatorial low-pressure region." Later the book writes that "Colder air causes a higher pressure." Not just this, when I plotted data between sea level pressure, and average temperature for a weather station in New York, the plot I got was this which seems totally counter-intuitive to the direct relationship suggested by the ideal gas law.

enter image description here

Can someone please help me fix this conundrum?

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  • $\begingroup$ as temperature increases, pressure decreases How did you reach that conclusion from $PV=nRT$? Is there a typo? $\endgroup$
    – G. Smith
    Jul 22, 2020 at 5:25
  • $\begingroup$ Was a typo, edited it $\endgroup$
    – Oishika
    Jul 22, 2020 at 5:35

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The ideal gas law takes no account of weather patterns over land and water; it takes no account of atmospheric circulation. So the connection you attempt to draw between the gas law and weather reporting is invalid.

Furthermore, the gas law's relationship between temperature and pressure you cite requires that the volume be held constant. No such rule obtains when describing air circulation patterns in the atmosphere.

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  • $\begingroup$ It's also worth pointing out that ideal gas law is also not true for any real gas at moderate pressure and temperature. Though, the relationships are generally quite similar ($P\uparrow \implies T\uparrow$ when $V$ is constant), but there may not even be an exact mathematical form for it. $\endgroup$
    – user258881
    Jul 22, 2020 at 7:07
  • $\begingroup$ Also, air contains variable amounts of water vapour, which is not an ideal gas. $\endgroup$
    – PM 2Ring
    Jul 22, 2020 at 10:05
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    $\begingroup$ @PM2Ring you cannot say that water vapor is not an ideal gas. It may or may not behave like an ideal gas depending on concentration. For atmospheric water vapor see physics.stackexchange.com/questions/137491/… $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Jul 22, 2020 at 11:50
  • $\begingroup$ @GiorgioP Fair enough. I suppose the effects due to the variation of the humidity of the air are more important than its departure from ideal gas behaviour. $\endgroup$
    – PM 2Ring
    Jul 22, 2020 at 11:59
  • $\begingroup$ Thank you! Is the reason why the ideal gas law is not valid because the volume is not held constant? $\endgroup$
    – Oishika
    Jul 22, 2020 at 13:36

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