Particle model and pressure revision notes

This resource explicitly revises Particle model and pressure: Particle motion in gases, Pressure in gases (physics only), Increasing the pressure of a gas (physics only) (HT only). It connects particle spacing, particle motion, internal energy, density, gas pressure, state changes and calculation language so answers stay tied to the approved AQA Physics specification.

Particle Model of Gases and Pressure

1. Random motion of gas particles

• Gas particles are tiny, fast‑moving bodies that are in constant, random motion.
• Their speed and direction change continuously due to collisions with other particles and with the walls of the container.
• The kinetic energy of each particle is proportional to the square of its speed: \(E_k = \tfrac{1}{2}mv^2\).

2. Collisions with the container walls

• When a particle strikes a wall, it exerts a force on that wall for a very short time.
• The impulse delivered is equal to the change in momentum of the particle.
• Because collisions are frequent and random, the net effect is a continuous pressure on the walls.

3. Pressure as a force per unit area

• Pressure is defined as the normal force exerted by the gas on the wall divided by the area of that wall: \(P = \frac{F}{A}\).
• In the particle model, the force arises from the cumulative effect of many particle impacts.
• The magnitude of the force depends on two factors:

1. Frequency of collisions – how often particles hit the wall.
2. Momentum change per collision – related to the particle’s speed.

4. Temperature and kinetic energy

• Temperature is a measure of the average kinetic energy of the gas particles.
• Raising the temperature increases the average speed of the particles.
• Faster particles collide more often and with greater force, so the pressure rises if the volume is held constant.

5. Volume and collision frequency

• For a fixed mass of gas, decreasing the volume brings the walls closer together.
• Particles travel a shorter distance between collisions with the walls, so the collision frequency increases.
• At constant temperature, the increased collision frequency raises the pressure.
• Conversely, increasing the volume lowers the collision frequency and reduces the pressure.

6. The pressure–volume relationship (Boyle’s Law)

• For a fixed amount of gas at constant temperature, the product of pressure and volume is constant:

\(P\,V = \text{constant}\).

• This can be written as \(P_1V_1 = P_2V_2\) when comparing two states.
• The relationship is a direct consequence of the particle model: reducing volume increases collision frequency, while increasing volume decreases it.

7. Work done on a gas and energy transfer

• When a gas is compressed, work is done on it: \(W = P\,\Delta V\).
• This work increases the internal energy of the gas, which is reflected in a higher average kinetic energy (temperature) if the compression is rapid.
• The energy transferred to the gas is stored as increased kinetic energy of the particles, not as a separate form of energy.

8. Distinguishing key concepts

• Pressure vs. atmospheric pressure: Pressure is the force per unit area exerted by the gas on its container; atmospheric pressure is the external pressure exerted by the air outside the container.
• Temperature vs. thermal energy: Temperature is a measure of average kinetic energy; thermal energy is the total kinetic energy of all particles.
• Work done vs. energy transferred: Work done on a gas is a form of energy transfer that increases the gas’s internal energy.
• Energy vs. power: Energy is the total amount transferred; power is the rate of energy transfer (energy per unit time).

9. Practical applications

• Piston engines: Compression of air in a cylinder increases pressure and temperature, driving the piston.
• Air conditioning: Refrigerant gas is compressed and expanded to transfer heat.
• Balloon physics: Heating a balloon increases internal pressure, causing it to expand until equilibrium with external pressure is reached.

10. Summary of the particle model

• Gas particles move randomly and collide with each other and the walls.
• Collisions produce a measurable force on the walls, giving rise to pressure.
• Temperature controls particle speed; volume controls collision frequency.
• The product of pressure and volume remains constant for a fixed amount of gas at constant temperature.
• Work done on a gas transfers energy, raising its internal energy and temperature.

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Key Terms

• Particle model
• Random motion
• Collision
• Pressure
• Temperature
• Volume
• Boyle’s Law
• Work done on a gas
• Internal energy
• Atmospheric pressure

Exam Tips

• Remember the distinction between pressure and atmospheric pressure.
• Use the equation \(P_1V_1 = P_2V_2\) for quick calculations.
• When a problem mentions *constant temperature*, assume the internal energy of the gas does not change unless work is explicitly stated.
• Draw a simple diagram of a gas particle colliding with a wall to visualise force and pressure.
• Check units: pressure in pascals (Pa), volume in cubic metres (m³), temperature in kelvin (K) or °C.

Common Mistakes

• Confusing pressure with atmospheric pressure.
• Treating temperature as a force.
• Forgetting that volume changes affect collision frequency, not just particle speed.
• Using the wrong sign for work done on the gas (work done *on* the gas is positive).
• Ignoring the constant‑temperature condition when applying Boyle’s Law.