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Question

What would be the height of the atmosphere if the air density were decreased linearly to zero with height? ? Assume that at sea level the air pressure is 1.0 atm1.0 \text{~atm} and the air density is 1.3  kg/m31.3\text{~ kg/m}^3.

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Answered 1 year ago
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(b)\textbf{(b)} When the air density decreases linearly to zero with height, the atmospheric pressure will now be the same with the air pressure at sea level. Using the same equation to find the height of the atmosphere;

pair=po+ρgh{p_{air} = p_o + \rho g h}

Where po=pair{p_o = -p_{air}} so;

pair=pair+ρgh{p_{air} = -p_air + \rho g h}

2pair=ρgh{2p_{air} = \rho g h}

h=2pairρg{h = \dfrac{2p_{air}}{\rho g}}

h=2(1.01×105 Pa)1.3 kg/m3×9.81 m/s2{h = \dfrac{2(1.01 \times 10^5 \text{ Pa})}{1.3 \mathrm{~kg/m^3} \times 9.81 \mathrm{~m/s^2}}}

h=15.8 km{\boxed{h = 15.8 \text{ km}}}

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