Assumptions in the Kinetic Theory of Gases

The kinetic theory of gases is a model that explains the behavior and properties of gases based on the motion of their constituent particles, which are assumed to be small, hard spheres in constant motion. This theory makes several assumptions about the behavior of gas particles and their interactions.

Assumption: Molecular Collisions are Short in Duration

The correct answer to the given question is option 'B' - short in duration. In the kinetic theory of gases, it is assumed that molecular collisions are short in duration. Here's an explanation of why this assumption is made:

Particle Motion
- According to the kinetic theory, gas particles are in constant random motion, colliding with each other and the walls of the container they are in.
- The collisions between gas particles are assumed to be perfectly elastic, meaning that there is no net loss or gain of kinetic energy during the collision. The total kinetic energy of the system remains constant.

Short Duration of Collisions
- The assumption that molecular collisions are short in duration is based on the observation that gas particles move rapidly and erratically.
- Due to their high speeds, gas particles collide with each other and the container walls in a very short amount of time.
- These collisions happen in nanoseconds or even picoseconds, which is an extremely short duration.

Implications of Short Duration Collisions
- The short duration of collisions implies that gas particles spend most of their time in free motion rather than interacting with each other.
- As a result, the interactions between gas particles are considered to be negligible during most of the time.
- This assumption is valid for most gases under normal conditions because the distances between gas particles are much larger than their sizes, allowing them to move freely without significant mutual forces.

Conclusion
In summary, the kinetic theory of gases assumes that molecular collisions are short in duration. This assumption is based on the observation that gas particles move rapidly and erratically, colliding with each other and the container walls in a very short amount of time. The short duration of collisions implies that gas particles spend most of their time in free motion, and the interactions between them are considered to be negligible during most of the time. This assumption allows for the development of mathematical models to describe the behavior of gases and explain their macroscopic properties.