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Question: Answered & Verified by Expert
The quantity $\frac{\mathrm{PV}}{\mathrm{KT}}$ represents $(\mathrm{K}=$ Boltzmann constant)
PhysicsKinetic Theory of GasesMHT CETMHT CET 2020 (15 Oct Shift 1)
Options:
  • A number of moles of gas.
  • B kinetic energy of gas
  • C mass of the gas
  • D number of molecules of gas in one mole
Solution:
2012 Upvotes Verified Answer
The correct answer is: number of molecules of gas in one mole
$\mathrm{PV}=\mathrm{nRT}$ $\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}$ Number of molecules $=\mathrm{N}_{\mathrm{A}} \frac{\mathrm{PV}}{\mathrm{RT}}$ $=\frac{\mathrm{PV}}{\left(\mathrm{R} / \mathrm{N}_{\mathrm{A}}\right) \mathrm{T}}=\frac{\mathrm{PV}}{\mathrm{k}_{\mathrm{B}} \mathrm{T}}$
where, $\mathrm{k}_{\mathrm{B}}=$ Boltzmann constant.

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