Question

Which is larger, the average speed of a nitrogen molecule at 20oC or the speed of sound? Sound travels at 768 miles per hour at 20oC.

Answer 1

first calculate speed od nitrogen

root mean square speed = (3RT/M)^1/2

where, R = ideal gas constant = 8.3145 (Kg.m²/sec²) / (K.mol)

T = absolute tempreture = 20⁰C = 273.15 + 20 = 293.15 K

M = mass of mole of gas in kilogram = 28.0134 gm/mol = 28.0134 X 10^-3 kg/mol

Substitute value in above equation

root mean square speed of N₂ = [[3 X (8.3145 (Kg.m²/sec²) / (K.mol)) X (293.15 K)] / [(28.0134 X 10^-3 kg/mol)]]^1/2

= [261024.6 m²/s²]^1/2

= 510.9 m/s

N₂ have speed 510.9 m/s = 1142.85 miles per hour

and sound have speed 768 miles per hour thus Nitrogen speed is larger than sound speed.