estimate pressure of air molecules at 273 K , if mean square speed is

1.	estimate pressure of air molecules at 273 K , if mean square speed is 500m2/s2 and density of air is 6 kg/m3
Answer» estimate pressure of air MOLECULES at 273 K , if mean square speed is 500m2/s2 and DENSITY of air is 6 kg/m3 solution : we know from kinetic THEORY of gases, square mean root velocity of gas , $V_{rms}=\sqrt{\frac{3P}{\rho}}$ given, mean square , $V_{rms}^2$ = 500m²/s² taking square root of it to get rms velocity. i.e., $V_{rms}=\sqrt{500}=10\sqrt{5}$ density , ρ = 6 kg/m³ so, 10√5 = √{3P/6 } SQUARING both SIDES, 500 = 3P/6 or, 500 × 6/3 = P or, P = 1000 N/m² hence, pressure of air molecule is 1000 N/m² or Pascal.