π‘οΈ KINETIC THEORY OF GASES Β· KTG
Ideal gas β’ Pressure derivation β’ Kinetic energy β’ Degrees of freedom β’ Specific heats β’ Maxwell distribution β’ NEET problems
π IDEAL GAS EQUATION
PV = nRT (n = number of moles, R = 8.314 J/molΒ·K)
Also: PV = NkT (N = number of molecules, k = Boltzmann constant = 1.38Γ10β»Β²Β³ J/K)
R = NAk (Avogadro's number NA = 6.022Γ10Β²Β³ molβ»ΒΉ)
π POSTULATES OF KINETIC THEORY
- Gas consists of large number of molecules in random motion.
- Molecules are point masses (volume negligible).
- No intermolecular forces except during elastic collisions.
- Collisions with walls cause pressure.
- Average kinetic energy β absolute temperature.
β‘ PRESSURE & RMS SPEED
Pressure: P = (1/3) Ο vrmsΒ² = (1/3) (Nm/V) vrmsΒ²
RMS speed: vrms = β(3RT/M) = β(3kT/m)
Mean speed: vavg = β(8RT/ΟM) = β(8kT/Οm)
Most probable speed: vmp = β(2RT/M) = β(2kT/m)
π Maxwell speed distribution curve
π KINETIC ENERGY & TEMPERATURE
Average translational KE per molecule: Eavg = (3/2) kT
For 1 mole: U = (3/2) RT (monatomic ideal gas)
Internal energy depends only on temperature for ideal gas.
π― DEGREES OF FREEDOM (f) & EQUIPARTITION
Each degree of freedom contributes (1/2)kT of energy per molecule.
Monatomic (He, Ar)
f = 3 (translational)
U = (3/2)nRT
Cv = (3/2)R, Cp = (5/2)R, Ξ³ = 5/3 = 1.67
Diatomic (Oβ, Nβ)
At room temp: f = 5 (3 trans + 2 rot)
U = (5/2)nRT
Cv = (5/2)R, Cp = (7/2)R, Ξ³ = 7/5 = 1.4
Polyatomic (nonβlinear)
f = 6 (3 trans + 3 rot)
U = 3nRT
Cv = 3R, Cp = 4R, Ξ³ = 4/3 β 1.33
π RELATION BETWEEN Cp & Cv
Cp β Cv = R (molar specific heats)
Ξ³ = Cp/Cv = 1 + 2/f
For monatomic: Ξ³ = 5/3; diatomic: Ξ³ = 7/5; polyatomic: Ξ³ = 4/3.
π MEAN FREE PATH (Ξ»)
Average distance between collisions: Ξ» = 1/(β2 Ο dΒ² n) (d = molecular diameter, n = number density)
Also Ξ» = kT/(β2 Ο dΒ² P)
π‘ NEET TIPS & SHORTCUTS
- vrms = β(3RT/M) β use in pressure problems.
- For a mixture, average molar mass = total mass / total moles.
- Internal energy of ideal gas depends only on temperature.
- In adiabatic process, TVΞ³β1 = constant, PVΞ³ = constant.
β οΈ COMMON MISTAKES
- Using vrms formula with mass in grams instead of kg.
- Confusing degrees of freedom for different gases at different temperatures.
- Assuming Cp β Cv = R for solids/liquids (only for ideal gas).
- Forgetting that k = R/NA in energy equations.
π QUICK REVISION CARD
Ideal gas law: PV = nRT = NkT
vrms: β(3RT/M)
Average KE: (3/2)kT per molecule
Cp β Cv = R
Ξ³ = 1 + 2/f
Mean free path: Ξ» = 1/(β2 Ο dΒ² n)
π¬οΈ KINETIC THEORY OF GASES β’ NEET REVISION NOTES
πΈ NOTES PREVIEW
Preview of Kinetic Theory of Gases Notes
π₯ DOWNLOAD KINETIC THEORY OF GASES NOTES PDF
Download Kinetic Theory of Gases Revision Notes for NEET Physics PDF for quick revision and strong conceptual clarity. This chapter is important for understanding the microscopic behavior of gases and connects thermodynamics with molecular motion.
These Kinetic Theory of Gases handwritten notes PDF free download include ideal gas equation, RMS speed, degrees of freedom, equipartition of energy, and all important formulas, tricks, and PYQ-based concepts.
- Concept-based + formula-based questions in NEET
- RMS speed and ideal gas equation frequently asked
- Important link between Thermodynamics and molecular physics
- Easy scoring if formulas are clear
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π WEIGHTAGE ANALYSIS
1β2 Questions
RMS speed + gas laws
Moderate Weightage
Theory + numericals
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