## Thermodynamics and Kinetics Lecture 24 Notes: Statistical Mechanics

Overview

Today we really begin stat mech. The lecture will cost you 51 minutes.

Details

Pi = ke^-Ea/kt

KT measures thermal energy. The more temperature, the more energy.

q = sum (e^-Ei/kT) molecular partition

Q = sum (() canonical partition function

All thermodynamic functions can be derived from partition functions, or the summations. How are the molecules partitioned among the levels of the systm.

At OK, we have a perfect crystal in the ground state. THe partition function will be 1 (Eo0), and for everything else it will be zero.

Thus at OK, the probability of being in the ground state is 1 or 100%.

The lattice model has atoms at regular intervals of volume. Atomic volume, with a total volume. Zero translational energy. q trans = 10^30th. Q trans = 10^30 &Nths where N is the number of atoms.

Only distinguishible states count.

Q trans = q trans^N for dist. sttees

Q trans = q transN/N!

NlogN0-N Stirling Approxmination

Polymer configurations.

Degenrecy is different states with the same energy.

At any temperature, the lowest state is the most probable.

Q leads to all thermodynamics. U is an average energy. U = pi Ei = probability x energy

U = KT2 d ln Q/ dTN

A = -kT lnQ

Review

BRASS breathe relax aim sight shoot

BLISS blend low irregular small secluded

search silence segregate speed safeguard tag

Intermolecular Forces: ionic, hydrogen bonding, dipole dipole, VdW

1st Law dU=dW + dQ

2nd Law dS = dq rev/T

3rd law, oK – S=O