Playbook
Kinetic Theory of Gases
80 q - 1.96/paper - 14% HARD. Gas laws at 0%; the RMS-speed page is ratio work on v_rms ∝ √(T/M).
- Questions in the bank
- 80
- q/paper (2024–25 papers)
- 1.96
- Tagged HARD
- 14%
- Subtopics
- 3
Strand: Quick-Win
When you’ll see it
The RMS speed of gas molecules at a temperature, the average KE, degrees of freedom and specific heats, or an ideal-gas law.
How this chapter is tested
80 q at 1.96 a paper, 14% HARD. Gas Laws and Ideal Gas Equation (19 q) has never produced a HARD question. Average KE, Equipartition, and Specific Heats (25 q, 12%) is degrees of freedom: 3 for a monatomic gas, 5 for a diatomic, giving γ = 5/3 and 7/5.
Kinetic Theory — Pressure, RMS Speed, and Temperature is the biggest page (36 q, 22%), and nearly every question is one proportionality: v_rms = √(3RT/M), so v_rms ∝ √(T/M). Double the absolute temperature and the speed rises by √2; compare hydrogen with oxygen at the same temperature and the ratio is √16 = 4. These are ratio questions, answered by setting up the proportion rather than by computing either speed.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Ideal-gas law
PV = nRT. Keep T in kelvin.
RMS, mean and most-probable speed
v_rms = √(3RT/M), v_mean = √(8RT/πM), v_mp = √(2RT/M). All ∝ √(T/M).
Equipartition and γ
Energy ½kT per degree of freedom; C_v = (f/2)R, γ = 1 + 2/f.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Using Celsius in the ratio
v_rms ∝ √T with T in KELVIN. Raising 27 °C to 927 °C is 300 K to 1200 K — the speed doubles, it does not rise √(927/27) times.
Doubling the speed with the temperature
v_rms ∝ √T, so doubling T multiplies the speed by √2. To double the speed, T must be quadrupled.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Kinetic Theory of Gases notesDrill every kinetic theory of gases question
80 questions from the bank, scoped to 3 bundled subtopics.
Drill one subtopic at a time
The 3 subtopics this playbook covers, in catalog order.
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