Kinetic Theory of Gases: Practice Problem & Solution
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)
Solution Explained:
To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:
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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