Topic 1 Flashcards
What is Microstates?
Any one of many possible states of a system.
All microstates are equally probable
What is Macrostates?
The state the system is in.
A number of microstates that can form a particular macrostate tell us how probable a macrostate is
How do you describe microstates?
Using the binomial distribution
W = N!/(N-k)!k!
What is Stirling’s approximation?
An approximation for factorials
lnx! ~= xlnx-x
What is a Gaussian distribution?
W ~= Cexp(-2(k-n/2)^2/N)
What is a mole?
The amount of any substance that contains the same number of individual entities as the number of atoms in 12g of carbon 12(6.02x10^23)
n = m/Mr n=N/Na
What is thermodynamics microstates defined by?
A number of properties usually pressure, temperature and volume
What are extensive variables?
Mass and volume, scale with the amount of material
What are intensive variables?
Temperature and pressure are independent of the amount of material
What is a thermodynamic function of state?
A function of state is a variable that has a definite value
corresponding to a particular state.
Pressure, temperature, volume, mass and density ect can be measured without needing to know the history of how the gas got to its present state
What are equation of states?
An equation of state is an equation relating state variables. For example the ideal gas equation
What are NOT state functions?
Work done and heat.
They depend on the path taken ( do depend on knowing the history of how the gas reached its present state.
What is a good approximation to the actual state?
The most probable state of a large state is a good approximation to the actual state
What is the ideal gas equation?
pV =Nk_BT
pV =nRT
What is heat?
Heat is thermal energy in transit
What is temperature?
Temperature is a measure of the internal energy of the body
What is the zeroth law of thermodynamics?
If two bodies A and B are in thermal equilibrium with each other, and a third body C is in equilibrium with A, then C is also in equilibrium with B
What is the first law of thermodynamics
dU = đQ + đW
U is internal energy, Q is heat supplied to system and W is work done ON system
The work done on an expanding gas is given by đW = −pdV
How do you calculate the heat supplied and work down for ideal gas?
Constant Pressure
Constant Volume
Isothermal
What is a exact differential?
If a function f(x,y) has an exact differential df, then
Δ𝑓=∫d𝑓
between (x1,y1) to (x2,y2)
has a UNIQUE VALUE, independent of the path taken from (x1,y1) to (x2,y2)
THE INTEGRAL OF AN EXACT DIFFERENTIAL IS PATH INDEPENDENT
Give an example of an exact differential?
Functions of states
dU
What is an inexact differential
If a function f(x,y) has an inexact differential df, then
Δ𝑓=∫d𝑓
between (x1,y1) to (x2,y2)
has a VALUE, dependent of the path taken from (x1,y1) to (x2,y2)
THE INTEGRAL OF AN INEXACT DIFFERENTIAL IS PATH DEPENDENT
Give an example of an inexact differential ?
đQ
Why is partial derivates important in exact and inexact differentials?
An exact differential is path independent, it can be shown that
(𝜕^2 𝑓)/𝜕𝑥𝜕𝑦=(𝜕^2 𝑓)/𝜕𝑦𝜕𝑥
for any differentiable single-valued function f(x,y)
SO
d𝑓=𝐹_1 d𝑥+𝐹_2 d𝑦, it follows that
((𝜕𝐹_1)/𝜕𝑦)_𝑥=((𝜕𝐹_2)/𝜕𝑥)_𝑦
THIS APPLIES TO:
If p is a function of V and T (p = p(V,T)), d𝑝=(𝜕𝑝/𝜕𝑉)_𝑇 d𝑉+(𝜕𝑝/𝜕𝑇)_𝑉 d𝑇 Reciprocal theorem: if 𝑧=𝑧(𝑥,𝑦) (𝜕𝑧/𝜕𝑥)_𝑦=1/(𝜕𝑥\/𝜕𝑧)_(𝑦 ) Cyclic relation: (𝜕𝑧/𝜕𝑥)_𝑦 (𝜕𝑥/𝜕𝑦)_𝑧 (𝜕𝑦/𝜕𝑧)_𝑥=−1
What is the maximum number of microstates?
Wmax = N!/(N/2)!(N/2)!=Nln2 (Usinf Strilings approximation)
For large N
What is the total number of microstates?
- Integrate gaussian distribution
- Wt=Csqrt(πN/2)
(For large peak) The most probable microstate corresponds to the total number of ways
What is the natural log of the total number of microstates?
Wln2=lnWmax
