Lecture 9 - Ideal Gas in Grand Canonical Ensemble...

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1 Ideal Gas in Grand Canonical Ensemble (Continued) Probability of finding a subsystem with n particles where the average # of particles in that volume V is N We do not care what the energy of the subsystem is, so     energy integrated out // / ( , ) n n kT n kT E kT n P E n d e e d e Q         / 3 1 ! n n kT n V Pe n         33 / Now 1 ! n n kT n kT n kT n VV N e N e P e N n   Since kT N    ,   1 ! n N n P e N n Poisson Distribution 0 Normalized such that 1 n n P N P Now Compute Note that 0 ! 1 !! N N nP P Show that 1 n n nP N     11 1 0 0 1 Substitute 1 ! 1 1! ! Nn n nn Nm m m N m LHS nP e n N m n n m eN m N e N N m     
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2 Adsorption of a Perfect Gas onto a Surface Surface has 0 N adsorption sites (distinguishable) --- n gas molecules adsorbed on it. Molecules do not
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Lecture 9 - Ideal Gas in Grand Canonical Ensemble...

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