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
