Ch 2 · 2.1.2 Particle Model · O Level Physics 5054
Topic 2 of 9 in Thermal Physics — O Level Physics 5054 — 59 lessons.
Introduction
Everything is made of tiny particles: atoms, molecules, ions and electrons. How close they are, how strongly they pull on each other and how fast they move explain why solids are rigid, why liquids flow and why a bicycle tyre feels harder on a hot day. (Syllabus section 2.1.2.)
Key ideas — Particles in the three states
How this explains the properties from lesson 2.1.1:
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. In a solid, everyone is standing in a strict grid, holding hands tightly; you can wiggle your arms, but you can't move from your spot. In a liquid, the crowd is still packed tight, but people are sliding past each other to get to the bar, making the group flow. In a gas, everyone has left the floor and is sprinting wildly in straight lines, only bumping into walls or each other occasionally.
📖 Definitions
🔍 Worked example — Easy
A gas occupies a volume of 2.0 m^3 at a pressure of 1.0× 10^5 Pa. If the volume is reduced to 0.5 m^3 at a constant temperature, calculate the new pressure.
🔍 Worked example — Standard
A gas at 300 K has a pressure of 100 kPa. If the temperature is increased to 600 K while the volume remains constant, what is the new pressure?
🔍 Worked example — Exam-style
A gas is contained in a cylinder with a piston. The initial pressure is 2.0× 10^5 Pa and the volume is 500 cm^3. The piston is pushed in until the volume is 250 cm^3. Calculate the new pressure, assuming temperature is constant.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Temperature and particle motion
When a substance is heated, its particles move faster: the higher the temperature, the greater the average kinetic energy of the particles.
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. In a solid, everyone is standing in a strict grid, just vibrating slightly in place. In a liquid, people are moving around, sliding past each other but staying close. In a gas, everyone is sprinting wildly, bouncing off the walls and each other.
📖 Definitions
🔍 Worked example — Easy
A gas is held at a constant temperature. If the volume of the container is doubled, what happens to the pressure? Use p_1V_1 = p_2V_2 to show the relationship.
🔍 Worked example — Standard
A gas occupies a volume of 400 cm^3 at a pressure of 1.5× 10^5 Pa. If the volume is compressed to 250 cm^3 at constant temperature, calculate the new pressure.
🔍 Worked example — Exam-style
A gas is at a temperature of 27 ° C. Calculate the temperature in Kelvin (absolute scale) using the relationship T(K) = T(° C) + 273.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the new pressure of the gas. [2] (b) Describe, in terms of particles, why the pressure changes when the volume is decreased. [2] [4 marks]
Key ideas — Gas pressure
Gas particles move fast and collide with the walls of their container. Each collision pushes on the wall with a small force. Millions of collisions every second over the wall's area give a steady force per unit area: that is the gas pressure.
🧑🏫 Teacher's explanation
Imagine you are in a crowded, bouncy castle. If you and your friends are running around wildly, you will constantly bump into the inflatable walls. Each time you hit a wall, you give it a tiny push. Because there are so many of you hitting the walls every single second, the walls feel a steady, outward push. This 'push' is exactly what gas pressure is.
📖 Definitions
🔍 Worked example — Easy
A gas is contained in a cylinder with a cross-sectional area of 0.02 m^2. If the particles exert a total force of 40 N on the walls, calculate the pressure of the gas.
🔍 Worked example — Standard
A gas occupies a volume of 4.0 m^3 at a pressure of 1.5 × 10^5 Pa. If the volume is compressed to 2.0 m^3 at constant temperature, what is the new pressure?
🔍 Worked example — Exam-style
A gas at 300 K has a volume of 2.0 L and a pressure of 100 kPa. If the temperature is increased to 600 K while the volume is kept constant, calculate the new pressure.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Changing pressure, volume and temperature
Hold one quantity constant and see what happens to the other two.
🧑🏫 Teacher's explanation
Imagine a room filled with bouncy balls. If you make the balls move faster (increase temperature), they will hit the walls more frequently and with more force, which we experience as an increase in pressure. If you shrink the room (decrease volume) while the balls move at the same speed, they will hit the walls more often simply because there is less space to travel before a collision occurs.
📖 Definitions
🔍 Worked example — Easy
A gas occupies a volume of 2.0 m^3 at a pressure of 1.0 × 10^5 Pa. If the volume is compressed to 0.5 m^3 at a constant temperature, calculate the new pressure.
🔍 Worked example — Standard
A balloon is filled with gas at a pressure of 101 kPa and a volume of 3.0 L. If the balloon is placed in a vacuum where the external pressure drops to 50.5 kPa (keeping temperature constant), what is the new volume?
🔍 Worked example — Exam-style
A gas cylinder has a volume of 0.050 m^3 and a pressure of 2.0 × 10^6 Pa. If the temperature is doubled while the volume is held constant, what is the new pressure? (Assume the relationship between P and T is linear and 0 K is the starting point for this qualitative check).
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Boyle's law: $p_1V_1 = p_2V_2$
For a fixed mass of gas at constant temperature, pressure × volume stays the same:
🧑🏫 Teacher's explanation
Imagine a room filled with bouncy balls (gas particles) flying around randomly. Pressure is simply the result of these balls hitting the walls of the room. Every time a ball hits a wall, it exerts a tiny force. If you shrink the room (decrease volume) while keeping the temperature the same, the balls have less space to move around. This means they will hit the walls much more frequently. Because they hit the walls more often, the total force exerted on the walls per unit area increases, which we measure as an increase in pressure.\n\nThink of it like a crowded hallway. If you suddenly make the hallway half as wide (half the volume) but keep the number of people the same, people will bump into the walls much more often. This is the essence of Boyle's Law: when volume goes down, pressure goes up, provided the temperature doesn't change.\n\nMathematically, this is an inverse relationship. If you halve the volume, the pressure must double to keep the product p × V constant. This is why the graph of p vs V is a curve (a hyperbola) that approaches the axes but never actually touches them; you can never have zero volume or zero pressure in a real gas.
📖 Definitions
🔍 Worked example — Easy
A gas occupies a volume of 400 m^3 at a pressure of 100 Pa. If the volume is compressed to 200 m^3 at constant temperature, what is the new pressure?
🔍 Worked example — Standard
A sample of gas has a volume of 5.0 cm^3 and a pressure of 2.0× 10^5 Pa. If the pressure is increased to 5.0× 10^5 Pa at constant temperature, calculate the new volume.
🔍 Worked example — Exam-style
A cylinder contains gas at 3.0 atm and 120 cm^3. The piston is pushed in until the volume is 4.0 cm^3. Calculate the new pressure in atm.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Worked example
Example 1. A syringe holds 60\ cm^3 of air at a pressure of 100\ kPa. The plunger is pushed in slowly (so the temperature stays constant) until the volume is 20\ cm^3. Find the new pressure.
🔍 Worked example — Easy
A syringe contains 50 cm^3 of air at a pressure of 101 kPa. If the volume is reduced to 10 cm^3 at constant temperature, calculate the new pressure.
🔍 Worked example — Standard
A gas occupies 0.5 m^3 at a pressure of 2.0 × 10^5 Pa. If the pressure is increased to 5.0 × 10^5 Pa at constant temperature, find the new volume.
🔍 Worked example — Exam-style
A weather balloon is filled with 25 m^3 of helium at a pressure of 1.0 × 10^5 Pa. As it rises, the external pressure drops to 0.25 × 10^5 Pa. Assuming the temperature remains constant, calculate the new volume of the balloon.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) Close together, randomly arranged; they move around each other (slide past each other). (2) The lowest possible temperature, about −273 °C; the particles have the least possible kinetic energy. (3) The particles move faster, so they hit the walls more often and with more force; the force per unit area on the walls, the pressure, increases. (4) V_2 = 120 × 500/200 = 300\ cm^3.