Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

A given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T$. The mass of each molecule of the gas is $m$. Which of the following gives the density of the gas? (2016 - II)
$P/(kTV)$
$mkT$
$P/(kT)$
$Pm/(kT)$

Solution:

From the ideal gas equation $PV = NkT$, the number density is $n = \frac{N}{V} = \frac{P}{kT}$. The mass density $\rho$ is mass per unit volume, so $\rho = m \times n = \frac{Pm}{kT}$.

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