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Why isn't the graph a straight line but is rather curved ?


The graph you posted is of the barometric formula. Compared to the link I posted, your axes are swapped, but nevermind. It describes the exponential decay of atmospheric pressure with increasing altitude. As exponential functions are curved (in a linear axis scaling as yours), your graph is not a streight line. The physics behind this comes from the fact, that air is a compressible gas. Air in a certain altitude is compressed by the air above. If you climb up a little, there is less air above you. This leads to the air being less compressed, meaing lower pressure and also meaning its less heavy per volume.

If you follow your graph from the righthand side (1000 hPa at sea level), and travel to the left of your figure, you'll notice that you never hit the y-axis (which would be 0 hPa). If your graph was a streight line, you'd inevitably hit zero hPa. This would then be the sharp "upper border" of the atmosphere. But this does not exist. Atmosphere (and therefore air pressure) gets thinner and thinner, and does not abruptly end at zero pressure. That's why the international space station (ISS) - while being "in space" - still experiences a little air drag while circling around earth.

If you sat yourself on the bottom of the ocean, you'd experience a lot of water pressure, as you and the surrounding water are pressurized by weight of the water above you. Water is - in contrast to air - not a "compressible" fluid, meaning it has the same weight per volume, regardless of pressure. (Well this is not 100% correct. But at least 99.9% correct. Which is good enough for now.) Now, if you start to swim upwards, the pressure is becoming less, but water's density does not change. This would lead to a graph with a streight line. If you continue upwards - as mentioned in the previous example - you will eventually hit the "ceiling" of the fluid, as the pressure becomes zero. This is the surface of the water.

So, why is the graph curved? Because atmosphere doesn't have a upper surface. :-)

  • $\begingroup$ Thank you :) but I'm still confused . The air density is not constant but doesn't it change linearly with altitude ? If it does then this means that the gravitational field varies linearly with altitude . Am I thinking right ? $\endgroup$ – user65035 Mar 1 '18 at 12:09
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    $\begingroup$ @ZahraaKhalife: About gravity: Within the atmosphere you may consider gravity as constant. We are ~6400km away from earth's center, so a few hundred feet up or down have a neglegible effect. Even ISS's 400km altitude do not change gravity a lot. Their weightlessness comes from the fact, that they are going around earth really fast - like one cycle every ~93 minutes. This way, the centrifugal force counteracts gravity, and they seem to be floating around. $\endgroup$ – NightLightFighter Mar 1 '18 at 16:34
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    $\begingroup$ @ZahraaKhalife: About density of air: As we consider (for now) atmosphere to have equal temperature everywhere, air's density just changes the same way as pressure does. Starting, again, at sea level with 1000 hPa, you go up ~18000 ft, and you see that air pressure has halved. You now have 50% air below and 50% above you. Then you climb another 18000 ft, and, again, air pressure has halved. Now there is only 25% air above you. You go another 18000 ft... That's the fun with exponential decay. You may want to google "Archilles and the Tortoise". ;-) $\endgroup$ – NightLightFighter Mar 1 '18 at 17:05
  • $\begingroup$ Thank u :) But temperature isn't supposed to be constant since density is not constant so the denser the air , the more collisions done between air molecules and the higher temperature we get. $\endgroup$ – user65035 Mar 1 '18 at 19:05
  • $\begingroup$ I may need to read more about this topic since am still not convinced as to why should density of air vary exponentially if the gravity and temperature dont vary much with altitude in atmosphere $\endgroup$ – user65035 Mar 1 '18 at 19:08

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