PhysicsChapter 2: Statistical Mechanics and Thermodynamics
Average Translational Kinetic Energy
For an ideal gas, the average translational kinetic energy per molecule is: ⟨K⟩ = (3/2)kT
Definition
For an ideal gas, the average translational kinetic energy per molecule is: ⟨K⟩ = (32)kT The current FBISE assessment framework explicitly requires deriving and using this relation. ([Scribd][2])
Key Meaning of Temperature
Kinetic-theory equation: pV=(13)Nm⟨c²⟩ Ideal-gas equation: pV=NkT Therefore: (13)Nm⟨c²⟩ = NkT Cancel `N`: (13)m⟨c²⟩ = kT Multiply both sides by `32`: (12)m⟨c²⟩ = (32)kT But: (12)m⟨c²⟩ is average translational kinetic energy per molecule. Therefore: ⟨K⟩=(32)kT For N molecules: Ktotal=(32)NkT For `n` moles: Ktotal=(32)nRT Also: pV=(23)K_total For an ideal gas: **absolute temperature is directly proportional to average translational kinetic energy per molecule.**
Formula / Key Relation
**⟨K⟩=(32)kT Ktotal=(32)NkT Ktotal=(32)nRT**
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Review the key facts, formulas and checks before you move on.Average Translational Kinetic Energy
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TEMPERATURE
- `T ↑ → average translational KE ↑`
60-second revision
- `⟨K⟩ = 32 kT`
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