Show that the pressure exerted by the gas is two-third of the average

1.	Show that the pressure exerted by the gas is two-third of the average kinetic energy per unit volume of the gas molecules.
Answer» According to kinetic theory of gases, the P exerted by a gas density ρ and r.m.s. velocity v is given by P = \(\frac{1}{3}\)ρv² Mass per unit volume of gas = Density (ρ) Average K.E. of translation per unit of volume of the gas. \(E=\frac{1}{2}\)ρv² ^{\(\frac{P}{E}=\frac{\frac{1}{3}ρv^2}{\frac{1}{2}ρv^2}=\frac{2}{3}\)} P= \(\frac{2}{3}E\) = \(\frac{2}{3}\)× Average K.E. per unit volume.

Show that the pressure exerted by the gas is two-third of the average kinetic energy per unit volume of the gas molecules.

Answer»

According to kinetic theory of gases, the P exerted by a gas density ρ and r.m.s. velocity v is given by

P = \(\frac{1}{3}\)ρv²

Mass per unit volume of gas = Density (ρ)

Average K.E. of translation per unit of volume of the gas.

\(E=\frac{1}{2}\)ρv²

^{\(\frac{P}{E}=\frac{\frac{1}{3}ρv^2}{\frac{1}{2}ρv^2}=\frac{2}{3}\)}

P= \(\frac{2}{3}E\)

= \(\frac{2}{3}\)× Average K.E. per unit volume.

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Show that the pressure exerted by the gas is two-third of the average kinetic energy per unit volume of the gas molecules.

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