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Derive an expression for atmospheric pre...

Derive an expression for atmospheric pressure.

Text Solution

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1. All objects on the surface of the earh are subject to constant atmoshpheric pressure.
2. We know that the pressure is thrust (force) per unit area.
3. Atmospheric pressure `=("Force of the atmosphere")/("Surface are of the earth")`
`=("Weight of the atmosphere")/("Surface area of the earth")`
`=("Mass of atmosphere"xxg)/("Surface area of the earth")[Weight W=mg]`
`=("Density of atmosphere"xx"Volume of atmosphere"xxg)/("Surface of the earth")[because"Mass"="density"xx"volume"]`
`=(rhoxx"surface are of the"xx"height of the atmosphere"xxg)/("surface are of the earth")[because"Volume"="area"xx"height"]`
`=rhoxx"height of the atmospher"xxg`
`therefore"Atmospheric pressure"P_(@)=rhoxxhxxgrArrP_(@)=rhohg`
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Knowledge Check

  • Unit of atmospheric pressure is

    A
    Pascal
    B
    `N//m^(2)`
    C
    A or B
    D
    None

  • Atmospheric pressure P_(@)=

    A
    `hrhog`
    B
    `(hrho)/(g)`
    C
    `(hg)/(rho)`
    D
    `(rhog)/(h)`

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