question_answer

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:

                \[\text{d}=\frac{\text{MP}}{\text{RT}}\]   (Refer to page 5/22) or\[P=\frac{\text{dRT}}{\text{M}}\]. Hence, \[\frac{{{P}_{2}}}{{{P}_{1}}}=\frac{{{d}_{2}}{{T}_{2}}}{{{d}_{1}}{{T}_{1}}}\,\] or \[{{P}_{2}}=\frac{{{P}_{1}}{{T}_{2}}}{{{T}_{1}}}\,\left( \frac{{{d}_{2}}}{{{d}_{1}}} \right)\] \[=\frac{760\times 263}{273}\,\left( \frac{1}{10} \right)=73\cdot 2\,\text{mm}\text{.}\]