# Section c Flashcards

## Partition function for N particles

A system of many particles

we get the partition function of the system by multiplying together the partition functions of the component particles

Assuming distinguishable, independent, non-interacting particles

- We can write Q as the product

- Q = q1 x q2 x q3…

indistinguishable particles

- if two particles are swapped, we couldnt tell the difference

Indistinguishability

- particles of different types are intrinsically distinguishable ( He, Xe etc.)
- if in the solid state crystal lattice, they can be given an individual address
- if in the gas phase, they are free to move around and are indistinguishable
- if in the liquid phase, they are inbetween (dont need to know this for this course)

Q=q to the power N

If particles are indistinguishable then the arrangemnets that would otherise be different, are identicle and so this relationship is an overestimation. Since there are N ways of arranging N particles, the correction factor is 1/N!

- Q = q to the power N/N!

Partition function for one particle

the sum is over the states available to the one particle

Partintion function for N particles

The sum is over all the microstates available to the system donated by, Q

From Q

we can calculate entropy and internal energy

- entropy is related to the dispersal of energy
- the partition fucntion is a measure of the number of states that are thermally accessible

Calibrating the entropy scale

third law tells us that - the entropy of a perfect crystal at absolute zero is 0 - this allows us to calibrate our entropy scale

Residula entropy

sometimes a discrepancy between experimental values. An explanation is that the solid has some degree of disorder at T=0 K is non zero

Residual entropy in H2O

Due to proton disorder, a water molecule has 4 possible tetrahedral sites that might have a proton - or might not

- in principle there are 2 to the power 4 = 16 possibilities, but only 6 of them have exactly two protons