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The quantity \(\frac{pV}{kT}\), represents

The quantity \(\frac{pV}{kT}\), represents Correct Answer Number of molecules

Concept:

Kinetic theory of gases-

  • The kinetic theory of gases is a theoretical model that describes-
  • the molecular composition of the gas in terms of a large number of identical tiny particles called molecules. 
  • Further, this theory explains that gas pressure arises due to particles colliding with each other and the walls of the container.
  • The kinetic theory of gases also defines thermodynamic variables such as temperature,
  • viscosity, and thermal conductivity, and all these properties are related to the microscopic phenomenon.


Explanation:

From the ideal gas equation, we have-

PV = nRT       ...(i)

Multiplying and dividing RHS of equation (i) by NA

⇒ PV = nNA (R/NA) T

Where 

NA = Avagadro number(6.023 × 1023) &

N (Number of molecules) = nNA 

⇒ PV = NKT

⇒ N = PV/kT

Hence, option-4 is correct

Postulates of the kinetic theory of gases:

  • All gases are consist of a collection of a large number of tiny identical particles called molecules.
  • The volume of gas molecules is negligible as compared to the volume of the container.
  • So the volume of gas = volume of the container (Except 0 K)
  • There are no intermolecular forces that act between gas molecules.
  • Due to the absence of any interactions between molecules the Potential energy of ideal gas is zero.
  • So internal energy of ideal gas is perfectly translational K.E. of gas. 
  • It is directly proportional to absolute temperature.
  • The internal energy depends only and only on its temperature.

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