Past exam of the physics B course of the University of Cambridge / 2014 / Paper 1 / Section A / A2

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- Solution A2

Solution

The Maxwell speed distribution is proportional to

v^{2} e^{- m v^{2} / (2 k_{B} T)}

. Setting its logarithmic derivative to zero gives the most probable speed:

v_{mp} = \frac{2 k _{B} T}{m} = \frac{2 RT}{M} ≃ 3.95 \times 1 0^{2} m s^{- 1} .

Use molecular oxygen, with

M ≃ 0.032 kg mo l^{- 1}

, and

T = 300 K

.

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