💨 Kinetic Theory of Gases
Complete Chapter Notes
1. Equation of State of Perfect Gas
PV = nRT
- P = Pressure
- V = Volume
- T = Temperature (Kelvin)
- n = number of moles
- R = gas constant
2. Work Done in Compressing a Gas
W = ∫ PdV
For isothermal process:
W = nRT ln(V₂/V₁)
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3. Assumptions of Kinetic Theory
- Gas consists of large number of molecules
- Molecules are in random motion
- Collisions are perfectly elastic
- No intermolecular forces (ideal case)
- Volume of molecules negligible
4. Concept of Pressure
Pressure is due to continuous collision of gas molecules with container walls.
---5. Kinetic Interpretation of Temperature
Temperature is proportional to average kinetic energy.
KE ∝ T
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6. RMS Speed of Gas Molecules
vᵣₘₛ = √(3RT / M)
- Higher temperature → higher speed
7. Degrees of Freedom
Number of independent ways in which a molecule can move.
- Monoatomic: 3
- Diatomic: 5
- Polyatomic: 6
8. Law of Equipartition of Energy
Energy is equally distributed among all degrees of freedom.
Energy per degree = ½ kT
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9. Specific Heat of Gases
- Cv = heat at constant volume
- Cp = heat at constant pressure
Cp − Cv = R
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10. Mean Free Path
Average distance travelled between two collisions.
---11. Avogadro’s Number
N = 6.022 × 10²³ molecules/mol
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12. Important Points
- Ideal gas follows PV = nRT
- Temperature measures kinetic energy
- Gas pressure due to molecular collisions
- Higher temperature → higher molecular speed
- Cp is always greater than Cv
