According the kinetic theory of gases, which of the following relation between pressure (P) and volume (V) is correct? (M is mass and v is velocity of the gas particles)

option (3)

CONCEPT:

• Kinetic theory of gases: It states that all gaseous molecules remain under random and continuous motion and the velocity of the particles depends on the temperature.
  • Using this theory various properties like pressure, temperature, the energy of the molecules can be explained.
  • ​Hence, this theory is called the Kinetic Theory of gases which were developed by Clausius and Maxwell.

\(PV =\frac{1}{2}Mv^2\) 

Where M is the mass of the particle, V is the volume and v is the velocity of the particles.

EXPLANATION:

• According to Pascal's law, a gas transmits pressure equally in all directions and the pressure exerted by the gas is given by- 

\(P = \frac{1}{3} ρ v^2\)

we know that density = Mass/Volume

\(ρ=\frac{M}{V}\)

\(P=\frac{1}{3}{M}{V^2}v^2\)

• \(PV =\frac{1}{3}Mv^2\) is the correct relation according to the kinetic theory of gases.

Additional Information

Assumption of Kinetic Theory:

• Between two collisions a molecule moves in a straight path with a uniform velocity.
• During the random motion, the molecules collide with one other with velocity remains unchanged.
• The size of molecules is negligible compared to the distance between the molecules
• The molecules are in a state of continuous random motion and they move all the possible directions with all the possible velocity.