On the basis of kinetic theory of gases, the gas exerts pressure because its molecules
(a) continuou

Q: Why do we assume the collisions are perfectly elastic?

If the collisions were inelastic, the gas molecules would lose kinetic energy with every bounce. Over time, they would slow down and eventually settle at the bottom of the container, which contradicts our everyday observation that gases remain dispersed and maintain their pressure indefinitely.

Q: Does a single molecule exert pressure?

A single molecule exerts a tiny, instantaneous force during a collision, not a continuous pressure. Pressure is a macroscopic property that emerges from the time-averaged force of trillions of molecules continuously bombarding the wall.

Q: Why doesn't the wall move when hit by the molecules?

The mass of the container wall is astronomically larger than the mass of a single gas molecule. While momentum is conserved and transferred to the wall, the resulting velocity of the wall is practically zero.

Q: How does temperature fit into this picture?

Temperature is a measure of the average kinetic energy of the gas molecules. Higher temperature means the molecules move faster, hit the walls more frequently, and undergo a larger change in momentum per collision, resulting in higher pressure.

Q: What happens if the container is not a rigid box, like a balloon?

In a flexible container like a balloon, the internal pressure exerted by the gas molecules pushing outward is balanced by the atmospheric pressure pushing inward and the elastic tension of the balloon material.

Question

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules

Options:

(A) continuously lose their energy till it reaches wall

(B) are attracted by the walls of container

(C) continuously stick to the walls of container

(D) suffer change in momentum when impinge on the walls of container

Sigma Percentile · Accepted Answer

### The Invisible Chaos

Have you ever wondered why a balloon stays inflated or why a tire feels hard when you pump air into it? The answer lies in the invisible, chaotic world of gas molecules. According to the **Kinetic Theory of Gases**, a gas is composed of a vast number of tiny particles that are in a state of continuous, random motion. They zip around at incredibly high speeds, constantly colliding with each other and with the walls of their container.

### The Anatomy of a Collision

To understand how these tiny particles create a macroscopic force, let's zoom in on a single gas molecule. Imagine this molecule, with mass $m$, flying directly toward the wall of its container with a velocity $v$. Its initial momentum is simply the product of its mass and velocity:

$$p_i = mv$$

Now, a crucial postulate of the Kinetic Theory is that these collisions are **perfectly elastic**. This means that no kinetic energy is lost during the impact. When the molecule strikes the rigid wall, it bounces back with the exact same speed, but in the opposite direction. Its new velocity is $-v$, making its final momentum:

$$p_f = -mv$$

### Newton's Second Law in Action

Because the molecule's velocity changed direction, its momentum has changed. We can calculate this change in momentum ($\Delta p$) as the final momentum minus the initial momentum:

$$\Delta p = p_f - p_i = -mv - (mv) = -2mv$$

The molecule experienced a change in momentum of $-2mv$. But momentum must be conserved! This means that a momentum of $+2mv$ was transferred to the wall during the collision.

Now, let's bring in Sir Isaac Newton. His Second Law of Motion states that the rate of change of momentum is equal to the applied force ($F = \frac{\Delta p}{\Delta t}$). Every time a molecule bounces off the wall, it exerts a tiny, instantaneous force on it.

### The Macroscopic Result: Pressure

While the force from a single molecule is infinitesimally small, remember that there are trillions upon trillions of molecules inside the container. They are continuously bombarding every square inch of the walls. The collective, time-averaged force of all these countless collisions creates a steady, macroscopic push outward.

When we take this total force and divide it by the area of the wall, we get **Pressure** ($P = \frac{F}{A}$).

Therefore, the pressure exerted by a gas is not because the molecules are attracted to the walls, nor because they stick to them. It is entirely due to the fact that the molecules **suffer a change in momentum when they impinge on the walls of the container**, transferring force through relentless, elastic collisions.

Animated Solution for Physics - Thermodynamics: On the basis of kinetic theory of gases, the gas exerts pressure because its molecules

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Visualized Solution

$K in e t i c T h eor y P os t u l a t es$

$A pp r o a c hin g t h e W a l l$

$E l a s t i c C o l l i s i o n$

$C han g e in M o m e n t u m$

$F or ce an d P r ess u r e$

The Sigma Insight: Kinetic Theory of Gases

The Invisible Chaos

The Anatomy of a Collision

Newton's Second Law in Action

The Macroscopic Result

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