A sample of a perfect gas occupies a volume V at a pressure P and obsolete temperature T. The mass of each molecules is m, which of the following expression given the number of molecules in the sample?

Options

A. `P/(kTV)`
B. `mkT`
C. `P/(kT)`
D. `(Pm)/(kT)`

Answer

D

Explanation

Ideal gas equation `PV = nRT=m/M RT`
`(P)/(m//V) = (RT)/(M) implies P/(rho)=(RT)/(M)`
`implies rho=(PM)/(rRT) = (Pxx(mN_(A)))/(kN_(A)T) = (Pm)/(kT)`.