Kinetic Theory of Gases

Molecules in a gas do not share one speed — they have a whole distribution of them, and the three averages everyone quotes are three different numbers off the same curve. Pick a gas, set a temperature and a number density, and read the pressure straight out of PV = (1/3) N m v_rms^2. Then drag the threshold: the fraction of molecules faster than a given multiple of the rms speed is the same percentage for helium at 100 K and carbon dioxide at 1000 K alike.

What this gas isAir is mostly these two, which is why air molecules sit near 500 m/s

Gas

N2 · M = 28.0134 g/mol · m = 4.65173e-26 kg

Number density

2.65165e+25 per m3

v_p : v_bar : v_rms

1 : 1.12838 : 1.22474

Faster than the threshold

1.00 x v_rms = 493.169 m/s -> 39.16 %

PV = (1/3) N m v_rms^2 · one pressure, from the spine, with V = 1 m3 · k = 1.380649e-23 J/K exact, and R = k x NA is computed, never typed · the three speeds stand in fixed ratios for every gas at every temperature, which is why the last card never moves.

Temperature273.15 K

Number density2.65165

Speed threshold1.00 x v_rms

Gas5 gases

Published states5 presets

Most probable speed v_p = sqrt(2RT/M)

402.670 m/s

Mean speed v_bar = sqrt(8RT/(pi M))

454.365 m/s

RMS speed v_rms = sqrt(3RT/M)

493.169 m/s

Pressure P = (1/3) n m v_rms^2

100.000 kPa