Question 1: Explain how the motion of particles in a gas contributes to the pressure exerted on the container walls.

Answer: Particles move randomly and collide with the walls; each collision exerts a force, and the total force over area results in gas pressure.

Question 1: Define the term 'average particle speed' in the context of the kinetic theory of gases.

Answer: The average speed of particles in a gas, calculated over a large number of particles, representing typical particle velocity.

Question 2: Describe how increasing the temperature of a gas affects the average speed of its particles.

Answer: Increasing temperature increases the average kinetic energy and thus increases the average speed of the particles.

Question 1: A container of gas has particles with an average speed of 500 m/s at 300 K. If the temperature is increased to 600 K, what is the new average speed of the particles? (Assuming ideal behaviour and using the relation v ∝ √T)

Answer: v2 = v1 × √(T2 / T1) = 500 × √(600 / 300) = 500 × √2 ≈ 707.1 m/s

Question 2: Calculate the pressure exerted by 2 mol of gas in a 0.1 m³ container at a temperature of 400 K. Use the ideal gas law (PV = nRT), where R = 8.31 J/(mol·K).

Answer: P = (nRT) / V = (2 × 8.31 × 400) / 0.1 = (2 × 3324) / 0.1 = 6648 / 0.1 = 66480 Pa

Question 1: Design a simple experiment to investigate how temperature affects the pressure of a gas in a sealed container. Outline the key variables, safety precautions, and expected outcome.

Answer: Variables: temperature (independent), pressure (dependent), volume (constant), amount of gas (constant). Precautions include handling hot equipment carefully and ensuring the container can withstand increased pressure. Expect pressure to increase as temperature rises, demonstrating the direct relationship between temperature and pressure.

Question 1: A sealed syringe contains 0.5 mol of air at 300 K and 100 kPa. When the plunger is pulled out, the volume increases to 0.001 m³. Assuming temperature remains constant, what is the new pressure inside the syringe? (Use Boyle's Law: P1V1 = P2V2).

Answer: P2 = P1 × V1 / V2 = 100,000 × 0.0005 / 0.001 = 50,000 Pa

Question 2: Explain how the kinetic theory of gases accounts for the pressure changes when a gas is compressed rapidly versus slowly.

Answer: Rapid compression causes more frequent and forceful particle collisions, increasing pressure; slow compression allows particles to adjust gradually, resulting in less fluctuation.

Question 1: Describe how the kinetic theory explains the operation of a hot air balloon.

Answer: Heating the air inside the balloon increases particle speed, raising the pressure and volume, which makes the balloon less dense and causes it to rise.

Question 2: In what ways does understanding particle motion contribute to designing efficient refrigeration systems?

Answer: It helps in understanding how gases expand and compress, enabling the design of systems that optimise heat transfer and energy efficiency.