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Why pressure do not vary with respect to height incase a gas contained in a vessel and atmospheric air pressure varies with respect to height.

for example we consider constant pressure in a mercury barometer over the volume above mercury level, but pressure of merucry changes with respect to height, why pressure of gas wont change with respect to height in barometer.

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  • $\begingroup$ It is instructive to calculate the height over which you would expect a 1% change. Useful figure: $\rho_{\text{air,stp}} \approx 1.2 \,\mathrm{kg/m^3}$. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 14, 2019 at 3:32
  • $\begingroup$ why atmospheric pressure is calculated only by considering weight of air above earth surface? should we need to consider kinetic theory of gases also to measure atmospheric pressure. $\endgroup$
    – teja
    Commented Feb 14, 2019 at 3:36
  • $\begingroup$ It is instructive to calculate the scale height for a 1% change in pressure by both static weight and kinetic theory. Under what conditions do you expect them to give the same answer? How well are those conditions met for some allegedly typical point on the Earth's surface? $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 14, 2019 at 3:39
  • $\begingroup$ Im asking that whether atomspheric pressure is sum of pressures due to static weight pressure and kinetic pressure. $\endgroup$
    – teja
    Commented Feb 14, 2019 at 3:44
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    $\begingroup$ If that is the question you intend then you should probably edit for improved clarity. However, the point of the second suggested exercise is that under the right conditions (equilibrium, constant density and adiabatic lapse) you get the same answer from the two calculation. Because these are not two distinct pressures but two ways of expressing the same physics (though the connection between them is not necessarily obvious when you first encounter them). $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 14, 2019 at 4:24

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Actually you are asking about two different situations.

In the case of a mercury barometer, if it is constructed correctly, the only gas above the mercury liquid will be mercury vapor. In such case, the pressure at the gas-liquid interface will be the vapor pressure of mercury. That pressure will be independent of the height of gas above the liquid. Mercury will condense or evaporate as necessary to maintain that pressure as the liquid rises or falls in the cylinder. The interface pressure can rise or fall with changes in temperature since the vapor pressure is a function of temperature. At 21 degrees C the vapor pressure is .002 mm HG, so it is pretty small.

As stated in the comments, height differences in the laboratory is generally too small to cause a significant difference in gas pressure.

One example of a situation where its necessary to calculate gas pressure changing with height is in a gas well. To calculate pressure at the bottom of a well given the surface pressure for a well hundreds or thousand of meters deep, the change in pressure with depth must be taken into account. This necessarily involves numerical methods, because the temperature varies with depth and the density of the gas varies with pressure and temperature and the ideal gas law is not accurate enough to use with the pressures and temperatures involved.

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