Most Probable Speed | Santa Fe College - Edubirdie

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

2024
Views:

364

Pages:

3
Author:

Jabin F.

# Most Probable Speed → The value of speed for which probability is max d P(c) / dc = 0, d²P(c) / dc² < 0 d / dc (e^(-mc²/2kBT) c²) = 0 e^(-mc²/2kBT) c² - e^(-mc²/2kBT) (mc²/kBT) = 0 e^(-mc^2/2kBT)xc(2-mc^2/kBT) = 0 c = 0, sqrt(kBT/m), infinity => P(c) is non-zero & +ve at c = sqrt(2kBT/m) P(c) = 0 at c = 0 & c = infinity Cp = sqrt(dkBT/m) = sqrt(2NAkBT/NAM) Cp = sqrt(2RT/M) (NAM = M = molar mass) Most probable speed: dp/dc = 0 d/dc(e^(-mc^2/2kBT)c) = 0 e^(-mc^2/2kBT) - e^(-mc^2/2kBT)(mc^2/kBT) = 0 e^(-mc^2/2kBT)(1 - mc^2/kBT) = 0 c = ±sqrt(kBT/m), 1/∞ P(c) = 0 at c = ∞ P(c) ≠ 0 at c = sqrt(kBT/m) cp = sqrt(kBT/m) = sqrt(RT/m) c = sqrt(kBT/m)

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