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Mean-square and Rms Speed
The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: crms = √⟨c²⟩
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Mean-square and Rms Speed
What is it?
The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: crms = √⟨c²⟩
In simple words
- RMS is directly linked to molecular kinetic energy and pressure.
Recommended for Class 12
Full school-level explanation
The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: crms = √⟨c²⟩
Important Distinction
Gas molecules do not all move at the same speed. Suppose molecular speeds are: `c₁, c₂, c₃ ... cN` Mean-square speed is: ⟨c²⟩ = c₁²+c₂²+...+cN²N RMS speed is: crms = √[c₁²+c₂²+...+cN²N] RMS speed is not generally the same as ordinary average speed. Because pressure depends on squared velocity components, RMS speed appears naturally in kinetic theory. From: p=(13)ρ⟨c²⟩ and: crms²=⟨c²⟩ we get: p=(13)ρc_rms² Therefore: crms=√(3p/ρ)
Formula / Key Relation
**crms = √⟨c²⟩** **crms = √(3p/ρ)**
Remember
- p=(13)ρ⟨c²⟩
- crms²=⟨c²⟩
- p=(13)ρcrms²
- crms=√(3p/ρ)
- crms = √⟨c²⟩
- crms = √(3p/ρ)
Deeper understanding
Go deeper on Mean-square and Rms Speed: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
RMS
Exam focus
Quick revision
- p=(13)ρ⟨c²⟩
- crms²=⟨c²⟩
- p=(13)ρcrms²
- crms=√(3p/ρ)
- Important Distinction: Gas molecules do not all move at the same speed. Suppose molecular speeds are: `c₁, c₂, c₃ ... cN`
- Formula / Key Relation: **crms = √⟨c²⟩** **crms = √(3p/ρ)**
For long answers on Mean-square and Rms Speed: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- p=(13)ρ⟨c²⟩
- crms²=⟨c²⟩
- p=(13)ρcrms²
- crms=√(3p/ρ)
Important formulas
- p=(13)ρ⟨c²⟩
- crms²=⟨c²⟩
- p=(13)ρcrms²
Common exam traps
- Do not calculate:
- `(average speed)²`
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not calculate:
- Mistake
`(average speed)²`
- Mistake
and call it mean-square speed.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
p=(13)ρ⟨c²⟩
crms²=⟨c²⟩
p=(13)ρcrms²
crms=√(3p/ρ)
The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: crms = √⟨c²⟩
p=(13)ρ⟨c²⟩
- Definition
- The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: crms = √⟨c²⟩
- Formula
- p=(13)ρ⟨c²⟩
- Critical warning
- Do not calculate:
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Exam Practice
Define
Q1. Define Mean-square and Rms Speed.
Explain
Q2. Explain: Important Distinction.
Example
Q3. Give one clear example of Mean-square and Rms Speed and say why it fits.
Mistake
Q4. State one common mistake students make about Mean-square and Rms Speed.
Exam note
Q5. Write a short exam note on Mean-square and Rms Speed: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.