Topic explanation

Standard explanation

The mean-square speed is the average of the squares of molecular speeds: ⟨c²⟩ The root-mean-square speed is: c_rms = √⟨c²⟩

Key points

• p=(13)ρ⟨c²⟩
• c_rms²=⟨c²⟩
• p=(13)ρc_rms²
• c_rms=√(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: **c_rms = √⟨c²⟩** **c_rms = √(3p/ρ)**
• RMS is directly linked to molecular kinetic energy and pressure.

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