Kinetic Theory

From ideal gas equation

where is pressure,
the volume,
the gas constant,
the temperature and
the number of moles.

Given pressure







We have mass atomic weight

From

Mean velocity of gas molecules

Volume of oxygen gas at STP
(i)
Volume of oxygen molecules at STP

Ideal gas equation is
As volume is constant
When
As doubles.

Let initial absolute temperature of gas be
New absolute temperature of gas,
Root mean square speed of molecules of gas is given by

At new absolute temperature, become times

The molecule of a monatomic gas has three translational degrees of freedom because it can move in space (3-dimensions) freely

At , , , ,

Step 1: Understanding Mean Free Path
The mean free path is the average distance a molecule in a gas travels before colliding with another molecule.
This concept is important in kinetic theory of gases and describes the behavior of molecules in a gas.
Step 2: Why Other Options are Incorrect
Option (b) refers to the distance between two molecules, which is different from the mean free path.

Option (c) refers to the distance a molecule travels before colliding with the wall, which is not the definition of the mean free path.
Option (d) is incorrect because the sum of distances traveled by all molecules does not relate to the mean free path.

Step 3: Conclusion Thus, the mean free path is the average distance a molecule travels without colliding.