Statistical Thermodynamics Flashcards
What is the Boltzmann equation?
S = k lnW
Where W = the number of configurations
What is Boltzmann’s constant?
k = 1.381 x 10^-23 JK-1
How many configurations are there when T = 0K?
Only one configuration possible
What happens to energy levels and hence entropy as a box expands, increasing volume?
Energy levels become closer together and so number of arrangements corresponding to the same total energy is greater when the energy levels are closely spaced.
Hence W increases, meaning entropy increases
What is residual entropy?
It is the entropy observed in a solid at T=0K which is due to positional disorder
If there are N molecules in a sample, how many possible configurations are there with the same energy when T=0K? (Residual entropy)
2^N possible configurations with the same energy
S = k lnW
S = k ln2^N = Nk ln2
What is the equation for the partition function q?
q = ∑i exp (- Ei / kT)
Where the sum is over all the states of the system
What is the use of the Boltzmann distribution?
It is used to calculate the relative numbers of molecules in two states separated in energy by ∆E.
It shows the most probable distribution of molecules in separate energy levels
How do electronic and rotational states differ with distribution of molecules?
The separation between different electronic states is usually large and hence most molecules are found in the lowest energy state.
Rotational energy states lie much closer together and so the populations of excited rotational states can be significant
What does the relative population of energy states depend solely on?
Temperature, at higher T more energy stated are populated.
Larger T results in a smaller fraction and hence a larger ratio for exp(- ∆E / kT)
What is the definition of q, the partition function?
q is the sum over the states, NOT levels. It is a measure of the thermally accessible states.
All energies are measured relative to ground states, as E0 = 0, so first term = 1
If T is 0 or infinite, what does this mean for q?
At T = 0, - Ei / kT = 0 so q = 1
At T = infinity, - Ei / kT = 0 so q = 1
At very extreme temperatures, what does q equal?
q = N states when T is extreme
(T is 0 or infinity)
At intermediate T, where kT is large compared to E1 and E2 but small compared to E3, what is partition function?
q = 1 + 1 + 1 + 0 + 0 + …
So q = 3
Are energy states thermally accessible when E < kT?
Yes, they are significantly thermally accessible
