Topic 1

Question 1

What is Microstates?

Answer 1

Any one of many possible states of a system.

All microstates are equally probable

Question 2

What is Macrostates?

Answer 2

The state the system is in.

A number of microstates that can form a particular macrostate tell us how probable a macrostate is

Question 3

How do you describe microstates?

Answer 3

Using the binomial distribution

W = N!/(N-k)!k!

Question 4

What is Stirling’s approximation?

Answer 4

An approximation for factorials

lnx! ~= xlnx-x

Question 5

What is a Gaussian distribution?

Answer 5

W ~= Cexp(-2(k-n/2)^2/N)

Question 6

What is a mole?

Answer 6

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

Question 7

What is thermodynamics microstates defined by?

Answer 7

A number of properties usually pressure, temperature and volume

Question 8

What are extensive variables?

Answer 8

Mass and volume, scale with the amount of material

Question 9

What are intensive variables?

Answer 9

Temperature and pressure are independent of the amount of material

Question 10

What is a thermodynamic function of state?

Answer 10

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

Question 11

What are equation of states?

Answer 11

An equation of state is an equation relating state variables. For example the ideal gas equation

Question 12

What are NOT state functions?

Answer 12

Work done and heat.

They depend on the path taken ( do depend on knowing the history of how the gas reached its present state.

Question 13

What is a good approximation to the actual state?

Answer 13

The most probable state of a large state is a good approximation to the actual state

Question 14

What is the ideal gas equation?

Answer 14

pV =Nk_BT

pV =nRT

Question 15

What is heat?

Answer 15

Heat is thermal energy in transit

Question 16

What is temperature?

Answer 16

Temperature is a measure of the internal energy of the body

Question 17

What is the zeroth law of thermodynamics?

Answer 17

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

Question 18

What is the first law of thermodynamics

Answer 18

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

Question 19

How do you calculate the heat supplied and work down for ideal gas?

Answer 19

Constant Pressure
Constant Volume
Isothermal

Question 20

What is a exact differential?

Answer 20

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

Question 21

Give an example of an exact differential?

Answer 21

Functions of states

dU

Question 22

What is an inexact differential

Answer 22

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

Question 23

Give an example of an inexact differential ?

Answer 23

đQ

Question 24

Why is partial derivates important in exact and inexact differentials?

Answer 24

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

Question 25

What is the maximum number of microstates?

Answer 25

Wmax = N!/(N/2)!(N/2)!=Nln2 (Usinf Strilings approximation)

For large N

Question 26

What is the total number of microstates?

Answer 26

• Integrate gaussian distribution
• Wt=Csqrt(πN/2)
  (For large peak) The most probable microstate corresponds to the total number of ways

Question 27

What is the natural log of the total number of microstates?

Answer 27

Wln2=lnWmax