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?
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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?

G1 Physics · Accepted Answer

Step 1: For N molecules, the ideal-gas equation is PV = NkBT, where kB is Boltzmann’s constant. Step 2: Hence number density N/V = P/(kBT). Step 3: Mass density ρ = total mass/volume = Nm/V. Step 4: Therefore ρ = Pm/(kBT). Final answer: (B).