question_answer

                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. If \[{{k}_{B}}\] is the Boltzmann's constant, then write the expression for the density of the gas.

Answer:

                According to kinetic theory of gases, \[P=\frac{1}{3}\rho \overline{{{\upsilon }^{2}}}=\frac{2}{3}\frac{\rho }{m}.\frac{1}{2}m\overline{{{\upsilon }^{2}}}\frac{2}{3}.\frac{\rho }{m}.\frac{3}{2}{{k}_{B}}T\] \[\therefore \] Density,                \[\rho =\frac{Pm}{{{k}_{B}}T}.\]