1.

A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule is m and kB is the Boltzmann’s constant, then write the expression for the density of the gas.

Answer»

According to kinetic theory of gases,

P = \(\frac{1}{3}ρv^2\)

\(\frac{2}{3}\frac{ρ}{m}.\frac{1}{2}mv^2\)

P = \(\frac{2}{3}\frac{ρ}{m}.\frac{3}{2}k_BT\)

∴ Density  \(ρ=\frac{Pm}{k_BT}\)



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