STATISTICAL MECHANICS BEH.410 Tutorial Maxine jonas February 14, 2003
STATISTICAL MECHANICS BEH.410 Tutorial Maxine Jonas February 14, 2003
Why Statistical Mechanics Understand predict the physical properties of macroscopic systems from the properties of their constituents Deterministic approach ma=F need of 6N coordinates at t r: and u but typically n= moles (1023)! “ Ensemble” rather than microscopic detail and its surroundings microcanonical, canonical, grand canonical
Why Statistical Mechanics? Understand & predict the physical properties of macroscopic systems from the properties of their constituents Deterministic approach - n e e d o f 6N coordinates at t 0: ri and vi - b u t t y p i c a l l y N ≡ moles (1023) ! “Ensemble” rather than microscopic detail … and its surroundings ¾microcanonical, canonical, grand canonical
What with Statistical mechanics? Averages, distributions, deviation estimates of microstates: specification of the complete set of positions and momenta at any given time ( points on the constant energy hypersurface for Hamiltonian dynamics Ensemble average ergodic hypothesis A=(numbe va(e)=iIF a(x(t))dt T time, will visit all possible microscopic states availableto ant of A system that is ergodic is one which, given an infinite amo
What With Statistical Mechanics? Averages, distributions, deviation estimates… … of microstates: specification of the complete set of positions and momenta at any given time (points on the constant energy hypersurface for Hamiltonian dynamics) Ensemble average & ergodic hypothesis: A system that is ergodic is one which, given an infinite amount of time, will visit all possible microscopic states available to it
The first Law- Work Work, heat energy basic concepts Energy of a system = capacity to do work At the molecular level, difference in the surroundings Energy transfer that makes use of Heat chaotic molecular motion Work .organized molecular motion △U=q+w state function -independent of how state was reached
The First Law – Work Work, heat & energy = basic concepts Energy of a system = capacity to do work ¾ At the molecular level, difference in the surroundings state function – independent of how state was reached Energy transfer that makes use of… Heat … chaotic molecular motion Work … organized molecular motion
Second law- Gibbs Spontaneous processes increase the overall"disorder of the universe Reasoning through an example microstates to achieve macrostate Gibbs postulate: for an isolated system, all microstates compatible with the given constraints of the macrostate Chere E,v and w are equally likely to occur Here 2 ways to distribute n molecules into 2 bulbs
Second Law – Gibbs Spontaneous processes increase the overall “disorder” of the universe Reasoning through an example - microstates to achieve macrostate Gibbs postulate: for an isolated system, all microstates compatible with the given constraints of the macrostate (here E, V and N) are equally likely to occur - Here 2N ways to distribute N molecules into 2 bulbs