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The density of air near earth's surface ...

The density of air near earth's surface is `1.3kgm^-3` and the atmospheric pressure is `1.0xx10^5Nm^-2`. If the atmosphere had uniform density, same as that observed at the surface of the earth what would be the height of the atmosphere to exert the same pressure?

Text Solution

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Let the uniform density be `rho` and atmospheric height be h. The pressure at the surfce of the earth would be
`p=rhogh`
`or 1.0xx10^5Nm^-2=(1.3kgm^-3)(9.8ms^-2)h`
`or, h=(1.0xx10^5Nm^-2)/((1.3kgm^-3)(9.8ms^-2))=7850m.`
Even Mount Everest (8848m) would have been outside the atmoshere.
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