Mean Speed Study Resources - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

359

Pages:

2
Author:

Jabin F.

Average speed or mean speed c̄ = ∫₀∞ P(c)cdc/ ∫₀∞ P(c)dc = ∫₀∞ e^(-mc²/2kBT) c²dc / ∫₀∞ e^(-mc²/2kBT) cdc c̄ = √(πkBT/2m) = √(πRT/2m) c̄² = 2kBT/m crms = √(2kBT/m) = √(2RT/m) p(c)dc = (m/(2πkBT)^(1/2) e^(-mc²/2kBT) dc p(c) = (m/(2πkBT)^(1/2) e^(-mc²/2kBT) => dP(c) / dc = 0, d^2P(c) / dc^2 < 0 most probable value → Cp = 0 c̄ = ∫₀∞ e^(-mc²/2kBT) cdc / ∫₀∞ e^(-mc²/2kBT) dc c̄ = √(2kBT/πm) = √(2RT/πm) => c̄² =∫₀∞ e^(-mc²/2kBT) c²dc / e^(-mc²/2kBT) dc c̄² = kBT/m crms = √(kBT/m) => crms>Z>Cp => all dimension

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