Question

At a certain altitude, the density of air is 1/10th of the density of the earth’s atmosphere and temperature is –10°C. What is the pressure at that altitude? Assume that air behaves like an ideal gas, has uniform composition and is at S.T.P. at the earth’s surface.

Answer 1

Given,  

The density of air is 1/10th of the density of earth's atmosphere and its temperature is -10°C.

Consider the air behaves as an ideal gas and it has uniform composition at STP at surface of the earth.

Then

$d\quad =\quad \frac { MP }{ RT } \quad$ and  $\quad P\quad =\quad \frac { dRT }{ M }$

Hence, $\frac { { P }_{ 2 } }{ { P }_{ 1 } } =\quad \frac { { d }_{ 2 }{ T }_{ 2 } }{ { d }_{ 1 }{ T }_{ 1 } }$

${ P }_{ 2 }=\left( \frac { { P }_{ 1 }{ T }_{ 2 } }{ { T }_{ 1 } } \right) \left( \frac { { d }_{ 2 } }{ { d }_{ 1 } } \right)$

${ P }_{ 1 }$ = atmospheric pressure = 760 mm Hg

$=\left( \frac { 760\quad \times \quad 263 }{ 273 } \right) \left( \frac { 1 }{ 10 } \right) \quad =\quad 73.2\quad mm$

The pressure at the altitude is 73.2 mm