Hear that, air?

An ideal gas of non-interacting helium atoms is in a thermal equilibrium at the temperature T=30CT = 30^\circ \mbox{C}. What's the probability that an atom in this gas has a speed near the speed of sound, i.e. has a speed in the range 340±5 m/s340 \pm 5~\mbox{m/s} ?

Details and assumptions

  • Mass of a helium atom is 6.646×1027 kg6.646 \times 10^{-27}~\mbox{kg}
  • The probability density as a function of energy for an atom in an ideal gas is p(E)=2kTπEkTexp(EkT) p(E) = \frac{2}{kT\sqrt{\pi}} \sqrt{\frac{E}{kT}} \exp({-\frac{E}{kT}}).
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