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Question: A sample of an ideal gas occupies volume V at a pressure P and absolute temperature. The mass of eac...

A sample of an ideal gas occupies volume V at a pressure P and absolute temperature. The mass of each molecule is m. Which of the following expressions gives the density of the gas ?

A

P/Kt

B

Pm/kT

C

m/kT

D

P/kTV

Answer

Pm/kT

Explanation

Solution

P = 13ρvrms2\frac{1}{3}\rho v_{rms}^{2} and

12mvrms2=32KTandC2=3KTmρ=3PC2=3Pm3KT=PmKT\frac{1}{2}mv_{rms}^{2} = \frac{3}{2}KTandC^{2} = \frac{3KT}{m}\rho = \frac{3P}{C^{2}} = \frac{3Pm}{3KT} = \frac{Pm}{KT}