Ideal Gas Laws
Senior 2 · Physics
Ideal Gas Laws
Lesson 1 of 5
18 min
You cannot see the air in a bicycle tyre, yet it holds up the bicycle, the rider and a sack of potatoes. A football pumped hard in the cool morning feels even harder by midday. An aerosol can carries the warning "Do not incinerate". All of these are gases obeying a small set of rules called the gas laws.
Before you meet the laws, you need a picture of what a gas is made of and the four quantities that describe it: pressure, volume, temperature and amount.
A gas is made of a huge number of tiny particles (atoms or molecules). The kinetic model describes them like this:
Pressure comes from those collisions with the walls. Each particle that hits a wall pushes on it for an instant. Billions of hits every second add up to a steady force on every square metre of wall.
Temperature measures how fast the particles move on average. The hotter the gas, the greater the average kinetic energy of its particles.
An ideal gas is a model: an imaginary gas that obeys the gas laws exactly. Its particles are assumed to:
Real gases such as air, nitrogen, oxygen and helium behave almost ideally at ordinary pressures and temperatures. They depart from ideal behaviour at very high pressure (the particles are crowded, so their own volume matters) and at low temperature, close to the point where the gas turns into a liquid (the attractions between particles matter).
| Quantity | Symbol | SI unit | Other units you will meet |
|---|---|---|---|
| Pressure | P | pascal, Pa (1 Pa = 1 N/m²) | 1 kPa = 1000 Pa; 1 atmosphere (atm) = 101 325 Pa = 760 mmHg |
| Volume | V | cubic metre, m³ | 1 L = 1 dm³ = 1000 cm³ = 0.001 m³ |
| Temperature | T | kelvin, K | degrees Celsius, °C |
| Amount of gas | n | mole, mol | — |
If you cool a gas, its particles slow down and its pressure falls. Experiments show that, for every gas, the pressure would reach zero at about −273 °C. Nothing can be colder than this temperature, called absolute zero. The kelvin scale starts there: 0 K = −273 °C. One kelvin is the same size as one degree Celsius, so
T (in K) = θ (in °C) + 273
Worked examples: 27 °C = 27 + 273 = 300 K. −23 °C = −23 + 273 = 250 K. 373 K = 373 − 273 = 100 °C, the boiling point of pure water at sea-level pressure.
Air pressure is lower the higher you go, because there is less air above you. At sea level it is about 101 kPa. Kigali lies about 1500 m above sea level, where it is about 85 kPa.
Worked example: what force does the air in Kigali exert on one side of a desk top of area 0.50 m²? F = P × A = 85 000 Pa × 0.50 m² = 42 500 N, about the weight of four small cars! The desk is not crushed because air pushes up on the underside with almost the same force.
Open Gas Properties and choose the Ideal screen. Pump some particles into the box with the pump handle. Watch them bounce off the walls and read the pressure gauge. Use the heater under the box to add heat and watch the particles speed up and the pressure rise.
Tip
Kelvin, always. Before you use any gas law, convert every temperature to kelvin by adding 273. A gas at 0 °C has not lost all its volume or pressure. At 0 K it would have.
Picture the particles. In an explain-question, always say what the particles are doing: moving faster or slower, hitting the walls more or less often, hitting harder or more gently.
Convert to kelvin: (a) 27 °C, (b) −73 °C, (c) 0 °C.
Solution: Add 273. (a) 300 K, (b) 200 K, (c) 273 K.
Convert 350 K to degrees Celsius.
Solution: Subtract 273: 350 − 273 = 77 °C.
A classroom window pane measures 1.2 m by 0.50 m. Air pressure in Kigali is about 85 kPa. What force does the air exert on one side of the pane, and why does the glass not break?
Solution: Area = 1.2 × 0.50 = 0.60 m². F = PA = 85 000 × 0.60 = 51 000 N. The glass does not break because the air on the other side pushes back with an almost equal force, so the net force is nearly zero.
Use the particle model to explain why a gas exerts pressure on the walls of its container.
Solution: The particles move quickly and randomly and keep colliding with the walls. Each collision exerts a small force on the wall. The very large number of collisions every second produces a steady total force, and force per unit area is pressure.
State two assumptions of the ideal-gas model, and say when a real gas behaves least like an ideal gas.
Solution: Any two of: the particles have negligible volume; there are no forces between particles except in collisions; collisions are perfectly elastic; motion is random. A real gas is least ideal at high pressure and low temperature, near the point where it liquefies.
Remember
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