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

P/kT

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Pm/kT

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m/kT

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P/kTV

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Solution

The correct option is B
Pm/kT

$P = \frac{1}{3} ρ C^{2}$

Also~ $\frac{1}{2} m C^{2} = \frac{3}{2} k T o r C^{2} = \frac{3 K T}{m}$

Now, $ρ = \frac{3 p}{C^{2}} = \frac{3 P m}{3 k T} = \frac{p m}{k T}$

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

The correct option is B Pm/kT P=13ρC2 Also~ 12m C2=32 k Tor C2=3KTm Now, ρ=3pC2=3Pm3kT=pmkT

The correct option is B
Pm/kT

$P = \frac{1}{3} ρ C^{2}$

Also~ $\frac{1}{2} m C^{2} = \frac{3}{2} k T o r C^{2} = \frac{3 K T}{m}$

Now, $ρ = \frac{3 p}{C^{2}} = \frac{3 P m}{3 k T} = \frac{p m}{k T}$