Theme B — The Particulate Nature of Matter
B.3.3 Gas Laws — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 27 of 53 1 quiz
Lesson summary
B.3.3 Gas Laws — IB PHYSICS SL notes: State and apply Boyle's law, Charles's law and the pressure (Gay-Lussac) law, including the use of kelvin and the interpretation of their graphs.Ideal gas — it obeys PV ∝ T.P is the pressure in Pa, V the volume in m3 and T the thermodynamic t…
- Empirical laws
- Assumption
- What the symbols mean
- Halving the volume
- Higher temperature
- Particle explanation
Part 1 of 8State variables
Ideal gas
- Ideal gas it obeys PV ∝ T.
- P is the pressure in Pa, V the volume in m3 and T the thermodynamic temperature in K.
Combined
- PV/T = constant for a fixed mass of gas.
Empirical laws
- Boyle's, Charles's and Gay-Lussac's laws come from experiments holding one quantity constant.
Assumption
- Assumption the mass and number of molecules of gas are constant.
Kelvin
- T = θ + 273, and a temperature ratio only makes sense in absolute temperature.
Part 2 of 8Boyle's law: constant temperature
Boyle's law: constant temperature
Statement
- Statement for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume, P ∝ 1/V.
Equation
- P1V1 = P2V2.What the symbols mean: p1, V1 = pressure and volume before · p2, V2 = after; only for a fixed mass of gas at constant temperature
Halving the volume
- Halving the volume the pressure doubles.
Graphs
- P against V is a hyperbola that never touches either axis, and P against 1/V is a straight line through the origin.
Higher temperature
- Higher temperature the curve lies further from the origin.
Particle explanation
- Particle explanation in a smaller volume each molecule hits the walls more often, while the temperature and the average kinetic energy are unchanged.
Isothermal
- Isothermal the change must be slow enough for the gas to stay at the temperature of its surroundings.
Part 3 of 8Charles's law: constant pressure
Charles's law: constant pressure
Statement
- Statement for a fixed mass of gas at constant pressure, volume is directly proportional to the absolute temperature, V ∝ T.
Equation
- V1/T1 = V2/T2.
Graph
- V against T in kelvin is a straight line through the origin.
Celsius graph
- V against θ is a straight line crossing the axis at −273 °C, an early estimate of absolute zero;
- real gases liquefy first.
Particle explanation
- Particle explanation the faster molecules need a larger volume to keep the pressure constant.
Part 4 of 8Pressure (Gay-Lussac's) law: constant volume
Pressure (Gay-Lussac's) law: constant volume
Statement
- Statement for a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature, P ∝ T.
Equation
- P1/T1 = P2/T2.
Graph
- P against T in kelvin is a straight line through the origin.
Particle explanation
- Particle explanation faster molecules strike the walls harder and more often.
Examples
- Examples a sealed can in a fire can explode and tyre pressure rises on a long journey.
Part 5 of 8P–V diagrams
| Line on a P–V diagram | Meaning |
|---|---|
| Horizontal line | Change of volume and temperature at constant pressure |
| Vertical line | Change of pressure and temperature at constant volume |
| Curve along an isotherm | Change of pressure and volume at constant temperature |
| Curve between isotherms | Change of pressure, volume and temperature |
- Isotherm
- a line of constant temperature on a P–V diagram.
Part 6 of 8Using the laws
1
Identify what is constant: temperature, pressure or volume.
2
Convert all temperatures to kelvin.
3
Use absolute pressures, not gauge pressures.
4
Use the same units for the initial and final values of P and V, since they cancel in ratios.
Choosing a law
- Choosing a law look at which quantity is kept constant.
Constant k
- Constant k it is nR or NkB, not to be confused with the Boltzmann constant.
Combined
- P1V1/T1 = P2V2/T2 when all three change.
Part 7 of 8Validity and experiments
Real gases
- Real gases they follow the laws at low pressure and high temperature, and deviate at high pressure or low temperature, eventually condensing.
Boyle's law test
- Boyle's law test trap air with oil, change the pressure slowly with time to settle and plot P against 1/V.
Pressure law test
- Pressure law test heat a flask in a water bath slowly, read the pressure and plot P against T in kelvin.
Errors
- Errors trapped heat, leaks and measuring the water temperature instead of the gas, so stir and wait for equilibrium.
Part 8 of 8More from the specification
More from the specification
Collisional pressure of gas atoms
- Collisional pressure of gas atoms momentum changes of colliding atoms striking container boundaries provide an analytical means to verify Boyle's law.
Ideal Gas Equation of State
- The macroscopic behaviour of an ideal gas is described by PV = nRT = N kB T, relating pressure P, container volume V,
- and absolute temperature T to the amount of substance in moles n.
Kinetic Theory of Gas Pressure
- Gas pressure results from countless elastic collisions of gas molecules against container walls; the rate of momentum change during collisions exerts a perpendicular force per unit area.
- (delta_p / delta_t)
Root-Mean-Square Speed and Temperature
- According to kinetic theory, absolute temperature is directly proportional to mean molecular kinetic energy: (1/2) m = (3/2) kB T, establishing that higher temperatures increase molecular speeds.
Avogadro's Hypothesis and Molar Proportionality
- Equal volumes of ideal gases at identical temperature and pressure contain an equal number of particles,
- meaning volume is directly proportional to the amount of gas in moles.
Gas pressure mechanism
- Gas pressure mechanism continuous collisions of moving gas molecules against container walls exert net perpendicular force per unit area.
Boyle's law pressure-volume
- Boyle's law pressure-volume for a fixed mass of gas at constant temperature, pressure is inversely proportional to container volume.
Charles's law expansion
- Charles's law expansion volume of an enclosed gas expands in direct proportion to absolute temperature when pressure remains constant.
Theory
- A well-tested, wide-ranging explanation supported by evidence.
Momentum
- P = mv, a vector.
Force
- A push or pull measured in newtons.
Helium
- Product of the fusion of hydrogen in stars.
Collision
- Short interaction with large internal forces.
Kinetic theory
- Particles in constant random motion.
Avogadro constant
- The number of particles per mole, 6.02 × 10²³ mol⁻¹
Average speed
- Total distance divided by total time.
N = nNA
What the symbols mean: N = number of particles · n = amount (mol) · NA = Avogadro constant (6.02 × 1023 mol−1)
Key terms
| Term | Meaning |
|---|---|
| Boyle's law | Pressure is inversely proportional to volume at constant temperature |
| Charles's law | Volume is proportional to absolute temperature at constant pressure |
| Pressure (Gay-Lussac) law | Pressure is proportional to absolute temperature at constant volume |
| Isotherm | Line of constant temperature on a P–V diagram |
| Absolute zero | 0 K or −273 °C, the lowest possible temperature |
| Isothermal change | Change at constant temperature |
Avoid these mistakes
1
Using °C in the gas laws — use kelvin.
2
Using gauge pressure — use absolute pressure.
3
Applying a law when the amount of gas changes — the mass must be fixed.
4
Thinking P and V are proportional in Boyle's law — they are inversely proportional.
5
Confusing which quantity is constant in each law — Boyle T, Charles P, pressure law V.
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