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Derivation of Gas Pressure Equation
Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or p = (13)ρ⟨c²⟩ This relationship is explicitly part of the current FBISE summative SLO. ([Scribd][2])
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Derivation of Gas Pressure Equation
What is it?
Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or p = (13)ρ⟨c²⟩ This relationship is explicitly part of the current FBISE summative SLO. ([Scribd][2])
In simple words
- Molecular collisions + isotropic motion produce the gas-pressure equation.
Recommended for Class 12
Full school-level explanation
Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or p = (13)ρ⟨c²⟩ This relationship is explicitly part of the current FBISE summative SLO. ([Scribd][2])
Formula / Key Relation
Consider a cube of side `L`. Take one molecule of mass `m` whose x-component of velocity is `cₓ`. For an elastic collision with a wall perpendicular to the x-axis: initial x-momentum: mcₓ final x-momentum: −mcₓ Magnitude of momentum change: Δp = 2mcₓ Time between successive collisions with the same wall: Δt = 2L/cₓ Average force from this molecule: F = ΔpΔt Therefore: F = mcₓ²/L For `N` molecules: F = (m/L)Σcₓ² Since wall area: A=L² pressure: p = FA so: p = Nm⟨cₓ²⟩/V For random isotropic motion: ⟨cₓ²⟩ = ⟨cy²⟩ = ⟨cz²⟩ and: ⟨c²⟩ = ⟨cₓ²⟩+⟨cy²⟩+⟨cz²⟩ Therefore: ⟨cₓ²⟩ = (13)⟨c²⟩ Hence: pV = (13)Nm⟨c²⟩ Since: ρ = Nm/V we also get: p = (13)ρ⟨c²⟩ pV = (13)Nm⟨c²⟩ p = (13)ρ⟨c²⟩
Remember
- pV = (13)Nm⟨c²⟩
- p = (13)ρ⟨c²⟩
Deeper understanding
Go deeper on Derivation of Gas Pressure Equation: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
`pV = ⅓ Nm⟨c²⟩`
Exam focus
Quick revision
- pV = (13)Nm⟨c²⟩
- p = (13)ρ⟨c²⟩
- Formula / Key Relation: Consider a cube of side `L`. Take one molecule of mass `m` whose x-component of velocity is `cₓ`.
- Molecular collisions + isotropic motion produce the gas-pressure equation.
- Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or **p = (13)ρ⟨
For long answers on Derivation of Gas Pressure Equation: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- pV = (13)Nm⟨c²⟩
- p = (13)ρ⟨c²⟩
- Formula / Key Relation: Consider a cube of side `L`. Take one molecule of mass `m` whose x-component of velocity is `cₓ`.
- Molecular collisions + isotropic motion produce the gas-pressure equation.
Important formulas
- pV = (13)Nm⟨c²⟩
- p = (13)ρ⟨c²⟩
Common exam traps
- Do not write:
- `⟨c⟩² = ⟨c²⟩`
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not write:
- Mistake
`⟨c⟩² = ⟨c²⟩`
- Mistake
in general.
- Mistake
Mean speed squared and mean-square speed are different quantities.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
pV = (13)Nm⟨c²⟩
p = (13)ρ⟨c²⟩
Formula / Key Relation: Consider a cube of side `L`. Take one molecule of mass `m` whose x-component of velocity is `cₓ`.
Molecular collisions + isotropic motion produce the gas-pressure equation.
Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or p = (13)ρ⟨c²⟩ This relationship is explicitly p
pV = (13)Nm⟨c²⟩
- Definition
- Kinetic theory relates gas pressure to the mean-square molecular speed through: pV = (13)Nm⟨c²⟩ or p = (13)ρ⟨c²⟩ This relationship is explicitly p
- Formula
- pV = (13)Nm⟨c²⟩
- Critical warning
- Do not write:
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Exam Practice
Define
Q1. Define Derivation of Gas Pressure Equation.
Explain
Q2. Explain: Formula / Key Relation.
Example
Q3. Give one clear example of Derivation of Gas Pressure Equation and say why it fits.
Mistake
Q4. State one common mistake students make about Derivation of Gas Pressure Equation.
Exam note
Q5. Write a short exam note on Derivation of Gas Pressure Equation: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.