Question

The pressure is exerted by the gas on the walls of the container because (A) It sticks with the walls (B) It is accelerated towards the walls (C) It loses kinetic energy (D) On collision with the walls there is a change in momentum

Short answer

The pressure exerted by the gas on the walls of the container is due to the change in momentum during collisions of gas particles with the walls (Option D). These collisions result in a net force applied to the wall, thus creating pressure.

Step-by-step solution

Pressure and Gas Particles

Pressure is defined as force applied per unit area, mathematically represented as: \(P = \frac{F}{A}\) In the case of gases, pressure is exerted on the walls of a container due to the continuous collision of gas particles with the wall. The force created due to these collisions results in pressure being exerted on the walls. Step 2: Evaluate option (A)

Gas Particles Sticking with the Walls

Gas particles are in constant motion and continuously collide with the walls of a container. However, they do not stick to the walls. They bounce off the walls and move in another direction after each collision. Thus, option (A) is incorrect. Step 3: Evaluate option (B)

Gas Particles Accelerated Towards the Walls

Gas particles move randomly in all directions inside the container. They are not specifically accelerated towards the walls. Although some gas particles might move towards the walls at any time, others are moving away from them. So, option (B) is incorrect. Step 4: Evaluate option (C)

Gas Particles Losing Kinetic Energy

The kinetic energy of gas particles is not lost during the collisions with the walls, as these collisions are considered elastic. In elastic collisions, the total kinetic energy of the system remains constant. So, option (C) is incorrect. Step 5: Evaluate option (D)

Change in Momentum During Collision

When gas particles collide with the walls of the container, their momentum changes. As per Newton's third law of motion, an equal and opposite force is applied to the wall during the collision, which results in a net force on the wall, contributing to the pressure exerted by the gas. This change in momentum is the main reason for the pressure exerted by gas particles on the container walls. Thus, option (D) is correct.

Key concepts

Kinetic Theory of Gases

The kinetic theory of gases helps us understand how gases behave on a molecular level. It focuses on the motion of gas particles and how they interact. According to this theory, gas particles are in constant, random motion, moving in straight lines until they collide with each other or with the walls of their container. These collisions are extbf{elastic}, meaning no kinetic energy is lost.

• Particles move randomly and freely.
• No energy is lost during collisions.
• Collisions with the container walls create pressure.

This vibrant motion and frequent collision explain why gas can fill any container shape and size they are placed in and how they exert pressure. By understanding and applying the kinetic theory, one can better grasp the nature of gases in different conditions and predict their behavior.

Momentum Change

Momentum is essentially a measure of the motion of an object and is calculated as the product of an object's mass and velocity. In the context of gases, when a gas particle collides with the container wall, its direction and velocity change, leading to a change in momentum. The change in momentum results from the force exerted during the collision. This force, as repeated collisions happen with many particles, builds up and creates pressure. The key points here include:

• Momentum is a product of mass and velocity.
• Change in momentum occurs due to collisions.
• This process is crucial in understanding pressure exertion in gases.

The exchange of momentum also leads to significant insights into how pressure in gases can be measured and manipulated in practical applications.

Elastic Collision

Elastic collisions are a critical concept when discussing the behavior of gases in a container. They imply that when gas particles collide with each other or with the walls of the container, they rebound with the same speed without losing kinetic energy. A few important attributes of elastic collisions are:

• Kinetic energy before and after the collision is the same.
• Both kinetic energy and momentum are conserved quantities.
• Such collisions allow the gas to maintain constant temperature and pressure over time.

This property ensures that gas particles continue to exert pressure consistently over time, which is fundamental to the understanding of gas behavior and pressure dynamics within a closed system.

Newton's Third Law

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. In the context of gas particles, when a particle strikes a wall, the force it exerts on the wall is met with an equal and opposite force by the wall on the particle. This interaction is pivotal in explaining how pressure is exerted by gases. Here are some takeaways:

• Each particle collision results in a small force on the wall.
• The cumulative effect of many such collisions leads to observable pressure.
• The law ensures balance and conservation within the system's interactions.

Understanding Newton's Third Law aids in comprehending the resistance and reactions observed in gases during collisions, helping students appreciate the broader principles of physics at play in everyday phenomena.