Question

The quantity $\left( {\dfrac{{PV}}{{{K_B}T}}} \right)$ represents the
A. Number of molecules in the gas
B. Mass of the gas
C. Number of moles of the gas
D. Translational energy of gas

Answer 1

Hint: Max Plank introduced the Boltzmann constant, which was named after Ludwig Boltzmann. It is a physical constant obtained by dividing two constants, the gas constant and the Avogadro number, by their ratio.

Complete answer:
As we know the ideal gas equation,
$PV = nRT$
Where, $P = $Pressure
$V = $Volume
$n = $Number of moles
$R = $Gas constant
$T = $Temperature
Using the above equation we get ,
$n = \dfrac{{PV}}{{RT}}$ $......1)$
We know that ,
$n = \dfrac{N}{{{N_A}}}$
$PV = \dfrac{N}{{{N_A}}}RT$$......2)$
Where $N$= number of molecules
${N_A} = $Avogadro’s number
$PV = NT\dfrac{R}{{{N_A}}}$
But $\dfrac{R}{{{N_A}}} = {K_B}$ is Boltzman constant
Substituting the above value in equation $2)$ , we get
Therefore, $PV = N{K_B}T$
$N = \dfrac{{PV}}{{{K_B}T}}$
Hence, $\dfrac{{PV}}{{{K_B}T}}$ represents the number of molecules.

Hence, the correct option is C. Number of moles of the gas.

Additional Information:
The Boltzmann constant is a proportionality factor that links the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It can be found in the definitions of the kelvin and gas constants, as well as Planck's law of black-body radiation and Boltzmann's entropy formula.
Applications: The Boltzmann Constant is used to indicate the equipartition of an atom's energy in classical statistical mechanics. It's a symbol for the Boltzmann factor. It has a remarkable impact on the statistical definition of entropy. It is used to denote thermal voltage in semiconductor physics.

Note:
When we are using the form of the ideal gas law with Boltzmann's constant, we have to use pressure in units of Pascal, volume in ${m^3}$ and temperature in $K$.