Kinetic Theory of Gases for NEET UG
Kinetic theory explains pressure and temperature as the result of countless tiny molecules in random motion. It links the gas laws to what molecules are actually doing.
PhysicsClass 1160 MCQs3 lessons11 flashcards3 memory tricks
Practise Kinetic Theory of Gases free
What you'll learn
- The ideal gas and the gas laws
Use PV = nRT to relate pressure, volume, temperature and amount of gas. - Pressure, temperature and molecular speed
Relate gas pressure and temperature to the kinetic energy and speed of molecules. - Degrees of freedom and specific heats
Use equipartition of energy to find the specific heats and γ of different gases.
Key formulas
| Ideal gas equation | PV = nRT = Nk_BT |
|---|---|
| Boyle's law (T fixed) | PV = constant |
| Charles's law (P fixed) | V/T = constant |
| Gay-Lussac's law (V fixed) | P/T = constant |
| Pressure | P = ⅓ρv²_rms |
| Average KE per molecule | KE = (3/2)k_BT |
| rms speed | v_rms = √(3RT/M) |
| Ordering of speeds | v_rms > v_avg > v_most probable |
Memory tricks
v_rms = √(3RT/M), v_avg = √(8RT/πM), v_mp = √(2RT/M), in the ratio √3 : √(8/π) : √2 ≈ 1.22 : 1.13 : 1.
A monoatomic gas has 3 degrees of freedom and γ = 5/3; a diatomic gas has 5 at room temperature and γ = 7/5. In general γ = 1 + 2/f.
Average KE per molecule = (3/2)kT for every gas. v_rms ∝ 1/√M, and M(O₂)/M(H₂) = 16, so H₂ is 4 times faster.
Try 3 NEET-style questions
Q1. The internal energy of 2 moles of a diatomic ideal gas at temperature T, ignoring vibration, is
- 3RT
- 7RT
- 5RT/2
- 5RT
Show answer
Answer: (4) 5RT
Each mole of a rigid diatomic gas has internal energy (5/2)RT. For 2 moles, U = 2 × (5/2)RT = 5RT.
Q2. The number of gas molecules in a sealed rigid container is doubled at the same temperature. The pressure of the gas
- halves
- stays the same
- becomes four times
- doubles
Show answer
Answer: (4) doubles
From PV = NkT, at fixed V and T, P ∝ N. Doubling the number of molecules doubles the pressure.
Q3. According to the law of equipartition, each vibrational mode of a molecule contributes an average energy of
- ½kT
- kT, since it has both kinetic and potential energy terms
- 3/2 kT
- zero
Show answer
Answer: (2) kT, since it has both kinetic and potential energy terms
A vibrational mode has two quadratic energy terms (kinetic and potential), each contributing ½kT. So each vibrational mode contributes kT.
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