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Average Translational Kinetic Energy
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])
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Average Translational Kinetic Energy
What is it?
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])
In simple words
- `⟨K⟩ = 32 kT`
Recommended for Class 12
Full school-level explanation
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
Remember
- absolute temperature is directly proportional to average translational kinetic energy per molecule.
- ⟨K⟩=(32)kT
- Ktotal=(32)NkT
- Ktotal=(32)nRT
Deeper understanding
Go deeper on Average Translational Kinetic Energy: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
TEMPERATURE
Exam focus
Quick revision
- absolute temperature is directly proportional to average translational kinetic energy per molecule.
- ⟨K⟩=(32)kT
- Ktotal=(32)NkT
- Ktotal=(32)nRT
- Key Meaning of Temperature: Kinetic-theory equation: pV=(13)Nm⟨c²⟩ Ideal-gas equation: pV=NkT Therefore: **(13)Nm
- Formula / Key Relation: ⟨K⟩=(32)kT Ktotal=(32)NkT Ktotal=(32)nRT
For long answers on Average Translational Kinetic Energy: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- absolute temperature is directly proportional to average translational kinetic energy per molecule.
- ⟨K⟩=(32)kT
- Ktotal=(32)NkT
- Ktotal=(32)nRT
Important formulas
- ⟨K⟩=(32)kT
- Ktotal=(32)NkT
- Ktotal=(32)nRT
Common exam traps
- Do not conclude heavier molecules have greater average translational KE at the same temperature.
- They move more slowly on average so that the kinetic-energy average remains the same.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not conclude heavier molecules have greater average translational KE at the same temperature.
- Mistake
They move more slowly on average so that the kinetic-energy average remains the same.
- Mistake
Do not conclude heavier molecules have greater average translational KE at the same temperature.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
absolute temperature is directly proportional to average translational kinetic energy per molecule.
⟨K⟩=(32)kT
Ktotal=(32)NkT
Ktotal=(32)nRT
For an ideal gas, the average translational kinetic energy per molecule is: ⟨K⟩ = (32)kT The current FBISE assessment framework explicitly requires deriv
⟨K⟩=(32)kT
- Definition
- For an ideal gas, the average translational kinetic energy per molecule is: ⟨K⟩ = (32)kT The current FBISE assessment framework explicitly requires deriv
- Formula
- ⟨K⟩=(32)kT
- Critical warning
- Do not conclude heavier molecules have greater average translational KE at the same temperature.
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Exam Practice
Define
Q1. Define Average Translational Kinetic Energy.
Explain
Q2. Explain: Key Meaning of Temperature.
Example
Q3. Give one clear example of Average Translational Kinetic Energy and say why it fits.
Mistake
Q4. State one common mistake students make about Average Translational Kinetic Energy.
Exam note
Q5. Write a short exam note on Average Translational Kinetic Energy: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.