NEET 2016 Phase 2 · PhysicsIdeal gasPrevious Year Question
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?
Answer: (B) Pm/(kT). Correct Answer (B): Pm/(kT) Using the ideal gas equation in its microscopic (kinetic-theory) form PV = Nk_BT, the number of molecules is N = PV/(k_BT).
- A.P/(kT)
- B.Pm/(kT)✓
- C.P/(kTV)
- D.mkT
Correct Answer
(B) Pm/(kT)
Solution & Explanation
Correct Answer (B): Pm/(kT) Using the ideal gas equation in its microscopic (kinetic-theory) form PV = Nk_BT, the number of molecules is N = PV/(k_BT). The total mass is Nm and density is mass per unit volume. Dividing by V cancels the volume, leaving ρ = Pm/(k_BT). Dimensionally this is correct: P/(k_BT) is number density (per m³) and multiplying by mass m per molecule gives mass per m³.
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