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# lec1 - Example Physical adsorption of a gas most of the...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Language: Probability 1st Law Microcanonical ensemble 2nd Law 3rd Law Canonical ensemble T=0 Quantum gases Grand Canonical Ensemble Phase Transitions Transport Processes 8.044 STATISTICAL PHYSICS I 8.044 L1B1
PROBABILITY Random variable (ignorance and/or QM) Continuous, discrete, or mixed Probability density: p ( x ) p x ( ζ ) Histogram (normalized) p(x) x PROB( ζ x < ζ + ) = p x ( ζ ) 8.044 L1B2

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p x ( ζ ) 0, p x ( ζ ) = 1, −∞ b PROB( a x < b ) = p x ( ζ ) a Cumulative probability: ζ d P x ( ζ ) −∞ p x ( ζ ) p x ( ζ ) = P x ( ζ ) Either p x ( ζ ) or P x ( ζ ) completely specifies the RV x . 8.044 L1B3
Example Physical adsorption of a gas

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Unformatted text preview: Example Physical adsorption of a gas most of the time ( when hot) x small fraction of the time (when hot) leaving the surface y z n v θ φ 8.044 L1B4 1 p( φ ) p(v) v 3 v 2 e 2 σ 2 2π 2π φ 3 σ 2 σ 4 σ = kT m v p( θ ) p(t) 2sin( θ )cos( θ ) π/ 2 θ τ t e 1 τ t τ 8.044 L 1B5a p( φ ) φ p(v) v p( θ ) θ p(t) t 2π π/ 2 τ 3 σ 1.0 1.0 1.0 1.0 P( φ ) P(v) P( θ ) P(t) 8.044 L1B5b PROB = p ( θ ) dθ p ( φ ) dφ = 2 sin( θ ) cos( θ ) dθ (1 / 2 π ) dφ d Ω = sin( θ ) dθdφ z x y θ φ d θ d φ d Ω PROB /d Ω = (1 /π ) cos( θ ) 8.044 L1B6 Gaussian density (memorize) p(x) ( x − x ) 2 1 p ( x ) = √ 2 πσ 2 e − 2 σ 2 x x + σ x h he = 0.61 h 1 2 2 parameters 8.044 L1B7...
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lec1 - Example Physical adsorption of a gas most of the...

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