The quantity $\frac{\mathrm{PV}}{\mathrm{KT}}$ represents $(\mathrm{K}=$ Boltzmann constant)

The quantity $\frac{\mathrm{PV}}{\mathrm{KT}}$ represents $(\mathrm{K}=$ Boltzmann constant)
  1. number of moles of gas.
  2. kinetic energy of gas
  3. mass of the gas
  4. number of molecules of gas in one mole

Solution

$\mathrm{PV}=\mathrm{nRT}$ $\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}$ 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.

Asked in: MHT CET 2020 (15 Oct Shift 1)

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