B.3
Gas Laws
Kinetic theory of ideal gases, pressure, the equation of state, Boyle's law, Charles' law, Gay-Lussac's law, pressure-volume diagrams, and internal energy of a monatomic ideal gas.
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Key Concepts, Gas Laws
Assumptions of the Kinetic Theory of Ideal Gases
The kinetic theory models a gas as a large number of identical point particles in continuous random motion. The key assumptions are: the molecules occupy negligible volume compared to the container; there are no intermolecular forces except during collisions; all collisions between molecules and with the container walls are perfectly elastic (kinetic energy is conserved); the time spent in a collision is negligible compared to the time between collisions; and the molecules move in random directions with a range of speeds. Real gases deviate from this model, but approximate ideal behaviour well at low pressure, moderate temperature, and low density, where molecules are far apart and interactions are minimal.
Pressure
Pressure is defined as the force per unit area acting perpendicular to a surface: P = F/A, measured in Pascals (Pa), where 1 Pa = 1 N/m². In a gas, pressure arises from the constant bombardment of the container walls by gas molecules. Each collision exerts a tiny force on the wall, and the cumulative effect of billions of collisions per second produces a measurable, steady pressure. Increasing temperature increases molecular speed and therefore the force and frequency of collisions, raising pressure. Decreasing the volume of a fixed amount of gas at constant temperature also increases pressure because collisions become more frequent.
Amount of Substance and Moles
The amount of substance n is measured in moles (mol). One mole contains exactly 6.02 × 10²³ particles (Avogadro's number, N_A). This is the link between the macroscopic world (moles, measurable in a lab) and the microscopic world (individual molecules). When using the ideal gas equation PV = nRT, n is the number of moles of gas. If you know the number of molecules N instead, you can use the equivalent form PV = NkT, where k is the Boltzmann constant and k = R/N_A.
The Ideal Gas Equation and the Gas Laws
The ideal gas equation is PV = nRT, where P is pressure in Pa, V is volume in m³, n is amount in moles, R = 8.31 J/mol/K is the universal gas constant, and T is temperature in Kelvin. This single equation contains all three gas laws as special cases. Boyle's law (constant temperature): PV = constant, so P₁V₁ = P₂V₂. Charles' law (constant pressure): V/T = constant, so V₁/T₁ = V₂/T₂. Gay-Lussac's law (constant volume): P/T = constant, so P₁/T₁ = P₂/T₂. All three were discovered experimentally before the full equation was derived, which is why the ideal gas law is said to be derived empirically.
Conditions for Ideal Gas Behaviour
Each gas law applies only when one variable is held constant. Boyle's law requires constant temperature (isothermal). Charles' law requires constant pressure (isobaric). Gay-Lussac's law requires constant volume (isochoric/isovolumetric). The full ideal gas equation PV = nRT handles all situations. A critical exam habit: always convert temperature to Kelvin before substituting into any gas law equation. Leaving temperature in Celsius is one of the most common sources of wrong answers in this topic.
Pressure-Volume Diagrams
A pressure-volume (P-V) diagram plots pressure on the y-axis against volume on the x-axis. An isothermal process (constant temperature) traces a hyperbola: as V increases, P decreases proportionally, so PV = constant. This gives a curved line called an isotherm. A higher isotherm represents a higher temperature. An isobaric process (constant pressure) is a horizontal line on a P-V diagram. An isochoric process (constant volume) is a vertical line. Being able to sketch and interpret these processes is a common Paper 2 skill.
Pressure from Molecular Collisions
The pressure a gas exerts on a container wall can be calculated from first principles using Newton's second law. When a molecule of mass m moving at speed u collides elastically with a wall, its momentum changes by 2mu. The force exerted equals this momentum change divided by the time between successive collisions with the same wall. For a molecule in a cubic box of side length L, the time between collisions is 2L/u, giving a force of mu²/L. Summing over all N molecules and averaging over all directions leads to the result: P = Nm<u²> / (3V), where <u²> is the mean square speed.
Internal Energy of a Monatomic Ideal Gas
For an ideal monatomic gas (atoms with no rotational or vibrational modes), all internal energy is translational kinetic energy. The average kinetic energy per molecule is (3/2)kT, where k is the Boltzmann constant and T is temperature in Kelvin. For N molecules, the total internal energy is U = (3/2)NkT. Since Nk = nR, this can also be written as U = (3/2)nRT. This means the internal energy of an ideal monatomic gas depends only on temperature. If temperature is constant (isothermal process), internal energy does not change. Any energy added must therefore leave as work done by the gas.
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Frequently Asked Questions, IB Physics Gas Laws
What is Gas Laws in IB Physics? ↓
Kinetic theory of ideal gases, pressure, the equation of state, Boyle's law, Charles' law, Gay-Lussac's law, pressure-volume diagrams, and internal energy of a monatomic ideal gas. This topic is part of Theme B (The Particulate Nature of Matter) in the current IB Physics syllabus.
Is Gas Laws SL or HL in IB Physics? ↓
Gas Laws is covered by both SL and HL students in the current IB Physics syllabus. HL students study additional depth and extension content beyond the SL core.
What equations do I need for IB Physics Gas Laws? ↓
The key equations for Gas Laws are covered in the concept tutorial above. For a structured set of notes with all equations, conditions and worked examples, the GradePod Exam Pack includes a revision note template for every topic.
What are common exam mistakes in IB Physics Gas Laws? ↓
Common mistakes are covered in detail in the exam technique video above. The GradePod Exam Pack also includes exam-style questions with mark schemes so you can see exactly how marks are awarded and where students typically drop them.
How do I revise Gas Laws for the IB Physics exam? ↓
Follow the GradePod three-step method. First, watch the concept tutorial and tick off each learning objective on the checklist above as you go. Second, watch the exam technique video to see how IB-style questions are answered under exam conditions. Third, use the Exam Pack to practise independently with knowledge questions, exam questions and mark schemes. That's it. It works. I promise.