The adiabatic heat gradient is determined as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\gamma = \frac{g}{c_{p}} [/tex]

where [tex]\gamma[/tex] is the rate that temperature falls when rising in an atmosphere. g is gravitational acceleration and [tex] c_{p} [/tex] is the heat apacity. On Earth it is 9.8 Kelvin per kilometer close to the surface of the Earth.

Remember that g has a negative centrifugal acceleration term like this

[tex]g = \frac{ G m}{r^{2}} - \frac{v^{2}}{r}[/tex]

where v is the speed due to rotation of the planet.

My question is if v should be determined only from Earths rotation around its axis or both from Earths rotation and the molecular motion in the gas.

If molecular motion is considered the value of g for air on Earth sinks by 0.95 % and the gravitational acceleration becomes

[tex]g = \frac{ G m}{r^{2}} - \frac{v^{2}}{r} - \frac{5 v_{rms}^{2}}{3 r}[/tex]

Where [tex] v_{rms} [/tex] is the root mean square speed of thermal motion on Earth approximately 500 m/s.

Do you understand how I derived the last term?

David

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# The adiabatic heat gradient is temperature dependent

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