question_answer

The density of air a t normal atmospheric pressure is \[1.293\text{ }kg\text{ }{{m}^{-3}}\]. What would be the density of air at a pressure of 10 atmospheres?

Answer:

Case - 1 (Normal atmospheric Pressure) \[{{d}_{1}}=1.293\text{ }kg\text{ }{{m}^{3}}\] \[{{P}_{1}}=1\text{ }atm.\] Case - 2 (Other than normal atmospheric pressure) \[{{d}_{2}}=?\text{ }R\text{ }D=?\] \[{{P}_{2}}=10\text{ }atm.\] We know, \[P=h\text{ }d\text{ }g\] For a given height at a place, h and g are constant. So, pressure formula changes as \[P\propto d\] \[\Rightarrow \]\[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{d}_{1}}}{{{d}_{2}}}\] \[\Rightarrow \]\[\frac{{{P}_{2}}}{{{P}_{1}}}\times {{d}_{1}}=\frac{10}{1}\times 1.293\]\[{{d}_{2}}=12.93\,kg\,{{m}^{-3}}\] Therefore, density of air at pressure 10 atm is \[12.93\text{ }kg\text{ }{{m}^{3}}.\]