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# Overview
In this course you will learn:
*Part 1: Orbits*
- Relevant formula for understanding orbits
- Get tricks to memorize and understand these formula
- Get an intuition for orbial manouvers
*Part 2: Light*
- Understaning the EM spectrum
- Understanding EM waves and their descriptions
- Various phenomena of EM waves
- Blackbody radiation
- Redshift
- Absorbtion
*Part 3: Atoms*
- Mass defect/ Fusion
- Energy levels
- Spectral lines
*Part 4: Heat*
- What are equilibria
- Ideal gas law
- Entropy
# Orbits
## Relevant formula
### General
$a_{zentri} = \frac{v_{\parallel}^{2}}{r} = \omega^{2}r$
_How to memorize:_
- Do unit analysis $\frac{m^{2}}{s^{2}} \frac{}{ m}= \frac{m}{s^{2}}$
- Smaller turn -> Larger centripetal force $\implies \propto \frac{1}{r}$
- Faster -> Larger centripetal force $\implies \propto v^{2}$
Why $\cdot r$ for the formula with $\omega$?
- Unit analysis
- Same angular velocity is much larger $v$ when far away
$F=ma$
### Newton
$\vec F_{G}= G\frac{mM}{r^{2}} \hat r$
_How to memorize_:
- Force needs to be $\propto$ $m$ and $M$ $\implies m \cdot M$
- Force is 'spread over the area of a sphere' $\propto \frac{1}{A} \propto \frac{1}{r^{2}}$
$E_{pot,G} = - G\frac{mM}{r} = \int_{\infty}^{x} F_{G} ds$
*How to memorize*:
- Applying a force over a distance takes _energy_
- Force $\cdot$ Distance = Energy $\implies \int F_{G}ds$
*Things to note*:
- $E_{pot,G}$ is
- allways negative
- minimal at the object
- zero at infinity
- You can always add different $E_{pot}$ and $F_{G}$ from different objects to get a total Energy/ Force.
- Sometimes it's usefull to first find $E_{pot}$ of the full system, and then calculate $F_{G}$ as $\vec F_{G}= -\nabla E_{pot}$
- $E_{pot,G}$ only is easy as long as you are outside of massive objects. If you are inside of a planet or star this changes.
- Only objects in a sphere below you actually pull you down.
- If you are in a sphere of mass, there is no gravity due to that sphere
### Keppler
$\frac{a^{3}}{T^{2}} = G\frac{M+m}{4\pi^{2}} \approx \frac{GM}{4\pi^{2}}$
_How to memorize_:
- Not super easy, but can be rationalized via unit analysis
- Reformulate as:
- $\frac{a}{T^{2}} = G \frac{M}{4\pi^{2}a^{2}}$
- $\frac{m}{s^{2}} = \frac{N}{kg}$ (From seeing that it has the same units as newtonian gravity but one mass is missing)
## Understanding elipses
Source: Wikipedia Krishnavedala
__image couldn't be loaded__
### Maths
Mathematically (don't worry about it):
$r= \frac{p}{{1+\epsilon cos \theta}}$
There are some general features and conceptual things that are useful to understand about elipses:
- For $\epsilon \to 0$ it is a circle.
- As you can see $\epsilon$ defines the 'elipsicity' of the elipse.
- $\cos \theta$ repeats every $2\pi$. So this deviation from the pueley circular path is like a pendulum
- This is relevant to understand lagrange points later on
$\epsilon = \frac{aphelion-perihelion}{aphelion+perihelion} = \frac{wobble range}{2 \cdot \textrm{major half axis}}$
$periapsis = a - \epsilon a$
$apoapsis = a + \epsilon a$
as can be seen the excentricity just says how much wobble we have on top of the semi-major axis
### Intuitions
Here you have a fixed star, and a planet orbiting it.
There are two very important points on the orbit:
- Aphelion (far)
- Perihelion (close)
Both points have the velocity *tangential* to the central object. (The only places where this happens)
Aphelion:
- Slowest speed
- We are "too slow" for a circular orbit here
Perihelion:
- Fastest speed
- We are "too fast" for a circular orbit here
This gives us some intuitions about orbital manouvers:
#### Hohman transfer
__image couldn't be loaded__
Von Leafnode - Own work based on image by Hubert Bartkowiak, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=1885233
_Process_:
1) Transform arbitrary point in inner orbit to periapsis
2) Go to apoapsis (we are now too slow for a circular orbit)
3) Boost until we are fast enough for circular orbit
4) Profit!
#### Circle drawing intuition
Given 2 body setup we can determine an orbit from the following information:
- Position
- Velocity vector
##### How can we do this intuitiveley?
Underlying intuitons:
- Velocity is always tangential to orbit
- Apoapsis and periapsis are the points where the planet starts 'switching direction'
_Easy case_:
Velocity is tangential
1) Are we faster than circular orbit here?
1) If yes -> Periapsis
2) If slower -> Apoapsis
3) If same -> Circular orbit
_Harder case_:
1) Separate velocity into tangential and radial:
2) If radial velocity > 0
1) We are moving towards apoapsis
### Advanced topics
#### Gravity assist
Idea:
Use momentum of planets to boost yourself.
Flying close to a planet is something like a "soft collision"
Analogy: (stolen from wikipedia)
- If you throw a tenisball against a train, it will pick up the trains speed
#### Lagrange points
Where do they come from?
- Go into system which rotates with the two major bodies
- Now we have two overlapping forces:
- Gravity of the two bodies
- Centrifugal force
- This leads to the following points.
- Note those points are all not fully stable
__image couldn't be loaded__
By Xander89, CC BY 3.0, Link
# Light
## The Spectrum
Light is electromagnetic radiation with a huge spectrum. It makes sense to get a general feel for the "types of light" there are:
Some special forms and their properties:
- Radio
- Long wavelength
- Weak interaction on molecular scales
- Low energy interactions
- Needs large antena/dishes
- IR:
- Interaction with vibrational structure of molecules
- Strongly dominated by Blackbody radiation
- Needs specific mirrors and optics
- Visible
- Intermediate wavelength
- Strong interaction with electronic structure of molecules
- Intermediate interactions
- Needs mirrors or optics
- UV:
- Interaction with high energy electronic structure of molecules (ionizing)
- Needs specific mirrors and optics
- X-ray
- Short wavelength
- Interacts with atomic structure
- High energy interactions
- Needs mirrors/ waveguides / fresnel plates
## Properties or EM waves
- Frequency
- Energy of photon
- Wavelength
- Intensity
Intensity is independent of frequency and wavelength!
### Formula
$\lambda \cdot f = c$ (Moving 1 wavelength every oscillation = full movement speed)
$E_{photon}= h f$
#### Wave equation
$\omega = 2\pi f$
$k = \frac{2\pi}{\lambda}$
$\vec E(t,x) = \vec E_{0} \sin (\omega t - k x + \phi) = \vec E_{0} \sin\left(2\pi f t - 2\pi \frac{f}{c}x + \phi \right)= \vec E_{0} \sin (2\pi f (t-\frac{x}{c}) + \phi)$
Understanding $t- \frac{x}{c}$.
This basically tells us how far the wave has progressed.
We can figure this out in two ways:
- How long ago was this light emmited?
- or
- How far away was it emmited -> calculate how long ago that was by dividing by $c$
#### Polarisation
You might have noticed above that the electric field $\vec E$ was written as a vector. This means that the light also has a _direction_.
This direction is always _orthogonal_ to the direction of propagation.
This direction is called the polarisation. There are many phenomena in nature that prefer certain types of polarisation. By understanding the polarisation of light we can probe those more eficiently.
In optics polarisation filters are built as follows:
*Sidenote*:
There is such a thing as circular polarisation. We will not discuss it further, but it is also relevant for some applications.
## Blackbody radiation
Hot objects radiate heat. This heat radiation has a specific spectral profile (a color so to say)
### Formula:
#### Stephan Boltzmann law:
How much energy lost due to heat (attention if we are radiating onto an other object, this object will also transfer some heat onto us (only relevant if we are approx equaly warm))
$\frac{E_{radiated}}{At} = \frac{P_{heat}}{A} = \sigma T^{4}$
Heat radiated per time and area $\propto$ $T^{4}$ (in $K$!!!)
if object is not perfect emiter:
$\frac{P_{heat}}{A}= \epsilon \sigma T^{4}$
$\sigma = 5.67 \cdot 10^{-8} W\cdot m^{-2} \cdot K^{-4}$
#### Wiens displacement law
From the peak of blackbody radiation to heat of object
$\lambda_{peak} = \frac{b}{T}$
with $b = 2.89777 \cdot 10^{3} m\cdot K$
## Light interactions
### Redshift/ Blueshift
$z = \frac{\lambda_{obs}-\lambda_{emit}}{\lambda_{emit}} = \frac{f_{emit}-f_{obs}}{f_{obs}}$ (note the flip between f and $\lambda$)
The easier formula are
$1 + z = \frac{\lambda_{obs}}{\lambda_{emit}} = \frac{f_{emit}}{f_{obs}}$
Blueshift: z < 0
Redshift: z > 0
#### Doppler shift
When an ambulance passes by the sound shifts. The same phenomenon occurs to light for objects that move relativeley to us.
$1+ z = \frac{\lambda_{r}}{\lambda_{s}}= \sqrt{\frac{1+\beta}{1-\beta}}$
With $\beta = \frac{v}{c}$ the fraction of speed of light.
Note this is for movement straight away from us
To get the sign right keep the following in mind:
- Moving away -> longer wavelengths -> redshift
- Moving towards us -> shorter wavelengths -> blueshift
Or if you prefer frequencies:
- Moving away -> less energy -> lower frequencies
- Moving towards us -> more energy -> higher frequencies
#### Cosmic redshift
In general this can be a confusing term so check the definition in the model used.
One convention is to calculate the cosmic redshift as $z = \frac{v_{recession}}{c}$
With $v_{rec}= H_{0}D$
This only actually holds for small redshifts, otherwise one would have to use the relativistic redshifts.
### Lambert beer law
If light interacts with an absorbtive medium the probability to be absorbed within the medium per length is constant.
From this we can derive an exponential decay of intensity as we go through a medium:
$\frac{I}{I_{0}} = e^{-\mu d}$
with $\mu$ the optical density. Sometimes we also write $\mu = \varepsilon c$ with $\varepsilon$ the molar absorbtion and c the molar concentration.
Alternativeley the log form says:
$\log_{10}\left(\frac{I_{0}}{I}\right)= A = \varepsilon d c$
With $A$ the absorbance
# Atoms
## Fusion
Combining certain atoms can release energy. This is similar to when you put two magnets together.
From $E=mc^{2}$ we know that energy is related to mass.
This means that we can calculate how much energy is released in a process if we measure the mass before and after.
The difference in mass is called _mass defect_
### Example:
$4 \cdot H \to He$
$m_{H}= 1.00784 u$
$4m_{H}= 4.03136u$
$m_{He}= 4.002602 u$
$\Delta m = 4 m_{H}-m_{He}= 0.028758 u = 4.78\cdot 10^{-29} kg$
$\Delta E = \Delta m c^{2} = 4.29\cdot 10^{-12} J$
Note the same also works in reverse when $U \to Fe$
## Energy structure
In the previous chapters we saw that the type of light (i.e. it's wavelength) is related to the energy of an individual photon.
$E_{photon}= \frac{hc}{\lambda}$
Due to quantum mechanical reasons electrons in atoms are confined to specific energy levels.
If we want to interact with those electrons we need to give them the correct amount of energy to transfer between two of those energy levels.
Those energy levels are often labeled in units of eV (electron volts)
$1eV = 1.60 \cdot 10^{-19}J$
$1eV = \frac{1239.8}{\lambda (nm)}$
Source: https://astro.unl.edu/naap/hydrogen/transitions.html
### Hydrogen like atoms:
$E(n) = \frac{R_{\infty}ch Z^{2}}{n^{2}}$
$R_{\infty}$: Rydberg constant $1.097 \cdot 10^{7} m^{-1}$
$Z$: Charge of core (1 for $H^{+}$)
$n$: The energy level
Now we know that $hf = \frac{hc}{\lambda} =^{!} \Delta E$
$\frac{1}{\lambda}= R_{\infty} Z^{2} (\frac{1}{n_{1}^{2}}- \frac{1}{n_{2}^{2}})$
__image couldn't be loaded__
These series are also experimentally visible:
# Heat
## Equilibrium
System tend to equilibrium, meaning that there is no imbalance left.
Ex.
- Putting a hot and a cool object in a room will lead to two medium warm objects.
- Putting helium in the left half of a room and hydrogen in the right half will lead to two halfs of the room both filled 50:50 by He and H
- etc
Exam tip:
- If you do not know why something happens
- -> Guess because of thermodynamics
- Why do black holes evaporate over time?
- -> Thermodynamics
- -> There needs to be involvement of heat -> heat -> blackbody radiation -> black holes need to radiate something -> hawking radiation!
## Gas
A gas is a collection of very looseley bound atoms/molecules. They are well described by
- Pressure $p$
- Volume $V$
- Number of particles: $n$
- Temperature $T$
These properties relate to eachother via the _Ideal gas law_:
$pV = nRT$
with $R=8.314 \frac{J}{K mol}$ the molar gas constant
### Intuition:
for $n,T$ const. (isothermal)
$p \uparrow \to V \downarrow$
for $n,V$ const (isochor)
$p \uparrow \to T \uparrow$
for $n, p$ const (isobar)
$V\uparrow \to T \uparrow$
## Entropy (bonus)
Entropy relates extractable heat to temperature.
$dS = \frac{dQ_{rev}}{T}$
Meaning the change in entropy is the change of heat at a specific temperature.
A completeley different approach to entropy is the number of 'equally labeled' states.
$S = k_{B} \ln \Omega$
Meaning that if I can give every single state a label $\Omega$ is small -> small entropy
If many states have the same label $\Omega$ is large -> high entropy
Ex.
- If I tell you my room is tidy. You know that there are not many states of the room I would call tidy. Ie $\Omega$ is small -> low entropy
- If I tell you my room is messy. There are a billion different ways my room can be messy. All of those different types of messy rooms are labeled as 'messy' ie $\Omega$ is large -> high entropy
### Relation
How do those two forms of entropy relate to eachother?
The intuition is: It's easier to clean a almost tidy room than it is to clean a room which is messy.
- This is relevant to understand lagrange points later on
$\epsilon = \frac{aphelion-perihelion}{aphelion+perihelion} = \frac{wobble range}{2 \cdot \textrm{major half axis}}$
$periapsis = a - \epsilon a$
$apoapsis = a + \epsilon a$
as can be seen the excentricity just says how much wobble we have on top of the semi-major axis
### Intuitions
Here you have a fixed star, and a planet orbiting it.
There are two very important points on the orbit:
- Aphelion (far)
- Perihelion (close)
Both points have the velocity *tangential* to the central object. (The only places where this happens)
Aphelion:
- Slowest speed
- We are "too slow" for a circular orbit here
Perihelion:
- Fastest speed
- We are "too fast" for a circular orbit here
This gives us some intuitions about orbital manouvers:
#### Hohman transfer
__image couldn't be loaded__
Von Leafnode - Own work based on image by Hubert Bartkowiak, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=1885233
_Process_:
1) Transform arbitrary point in inner orbit to periapsis
2) Go to apoapsis (we are now too slow for a circular orbit)
3) Boost until we are fast enough for circular orbit
4) Profit!
#### Circle drawing intuition
Given 2 body setup we can determine an orbit from the following information:
- Position
- Velocity vector
##### How can we do this intuitiveley?
Underlying intuitons:
- Velocity is always tangential to orbit
- Apoapsis and periapsis are the points where the planet starts 'switching direction'
_Easy case_:
Velocity is tangential
1) Are we faster than circular orbit here?
1) If yes -> Periapsis
2) If slower -> Apoapsis
3) If same -> Circular orbit
_Harder case_:
1) Separate velocity into tangential and radial:
2) If radial velocity > 0
1) We are moving towards apoapsis
### Advanced topics
#### Gravity assist
Idea:
Use momentum of planets to boost yourself.
Flying close to a planet is something like a "soft collision"
Analogy: (stolen from wikipedia)
- If you throw a tenisball against a train, it will pick up the trains speed
#### Lagrange points
Where do they come from?
- Go into system which rotates with the two major bodies
- Now we have two overlapping forces:
- Gravity of the two bodies
- Centrifugal force
- This leads to the following points.
- Note those points are all not fully stable
__image couldn't be loaded__
By Xander89, CC BY 3.0, Link
# Light
## The Spectrum
Light is electromagnetic radiation with a huge spectrum. It makes sense to get a general feel for the "types of light" there are:
Some special forms and their properties:
- Radio
- Long wavelength
- Weak interaction on molecular scales
- Low energy interactions
- Needs large antena/dishes
- IR:
- Interaction with vibrational structure of molecules
- Strongly dominated by Blackbody radiation
- Needs specific mirrors and optics
- Visible
- Intermediate wavelength
- Strong interaction with electronic structure of molecules
- Intermediate interactions
- Needs mirrors or optics
- UV:
- Interaction with high energy electronic structure of molecules (ionizing)
- Needs specific mirrors and optics
- X-ray
- Short wavelength
- Interacts with atomic structure
- High energy interactions
- Needs mirrors/ waveguides / fresnel plates
## Properties or EM waves
- Frequency
- Energy of photon
- Wavelength
- Intensity
Intensity is independent of frequency and wavelength!
### Formula
$\lambda \cdot f = c$ (Moving 1 wavelength every oscillation = full movement speed)
$E_{photon}= h f$
#### Wave equation
$\omega = 2\pi f$
$k = \frac{2\pi}{\lambda}$
$\vec E(t,x) = \vec E_{0} \sin (\omega t - k x + \phi) = \vec E_{0} \sin\left(2\pi f t - 2\pi \frac{f}{c}x + \phi \right)= \vec E_{0} \sin (2\pi f (t-\frac{x}{c}) + \phi)$
Understanding $t- \frac{x}{c}$.
This basically tells us how far the wave has progressed.
We can figure this out in two ways:
- How long ago was this light emmited?
- or
- How far away was it emmited -> calculate how long ago that was by dividing by $c$
#### Polarisation
You might have noticed above that the electric field $\vec E$ was written as a vector. This means that the light also has a _direction_.
This direction is always _orthogonal_ to the direction of propagation.
This direction is called the polarisation. There are many phenomena in nature that prefer certain types of polarisation. By understanding the polarisation of light we can probe those more eficiently.
In optics polarisation filters are built as follows:
*Sidenote*:
There is such a thing as circular polarisation. We will not discuss it further, but it is also relevant for some applications.
## Blackbody radiation
Hot objects radiate heat. This heat radiation has a specific spectral profile (a color so to say)
### Formula:
#### Stephan Boltzmann law:
How much energy lost due to heat (attention if we are radiating onto an other object, this object will also transfer some heat onto us (only relevant if we are approx equaly warm))
$\frac{E_{radiated}}{At} = \frac{P_{heat}}{A} = \sigma T^{4}$
Heat radiated per time and area $\propto$ $T^{4}$ (in $K$!!!)
if object is not perfect emiter:
$\frac{P_{heat}}{A}= \epsilon \sigma T^{4}$
$\sigma = 5.67 \cdot 10^{-8} W\cdot m^{-2} \cdot K^{-4}$
#### Wiens displacement law
From the peak of blackbody radiation to heat of object
$\lambda_{peak} = \frac{b}{T}$
with $b = 2.89777 \cdot 10^{3} m\cdot K$
## Light interactions
### Redshift/ Blueshift
$z = \frac{\lambda_{obs}-\lambda_{emit}}{\lambda_{emit}} = \frac{f_{emit}-f_{obs}}{f_{obs}}$ (note the flip between f and $\lambda$)
The easier formula are
$1 + z = \frac{\lambda_{obs}}{\lambda_{emit}} = \frac{f_{emit}}{f_{obs}}$
Blueshift: z < 0
Redshift: z > 0
#### Doppler shift
When an ambulance passes by the sound shifts. The same phenomenon occurs to light for objects that move relativeley to us.
$1+ z = \frac{\lambda_{r}}{\lambda_{s}}= \sqrt{\frac{1+\beta}{1-\beta}}$
With $\beta = \frac{v}{c}$ the fraction of speed of light.
Note this is for movement straight away from us
To get the sign right keep the following in mind:
- Moving away -> longer wavelengths -> redshift
- Moving towards us -> shorter wavelengths -> blueshift
Or if you prefer frequencies:
- Moving away -> less energy -> lower frequencies
- Moving towards us -> more energy -> higher frequencies
#### Cosmic redshift
In general this can be a confusing term so check the definition in the model used.
One convention is to calculate the cosmic redshift as $z = \frac{v_{recession}}{c}$
With $v_{rec}= H_{0}D$
This only actually holds for small redshifts, otherwise one would have to use the relativistic redshifts.
### Lambert beer law
If light interacts with an absorbtive medium the probability to be absorbed within the medium per length is constant.
From this we can derive an exponential decay of intensity as we go through a medium:
$\frac{I}{I_{0}} = e^{-\mu d}$
with $\mu$ the optical density. Sometimes we also write $\mu = \varepsilon c$ with $\varepsilon$ the molar absorbtion and c the molar concentration.
Alternativeley the log form says:
$\log_{10}\left(\frac{I_{0}}{I}\right)= A = \varepsilon d c$
With $A$ the absorbance
# Atoms
## Fusion
Combining certain atoms can release energy. This is similar to when you put two magnets together.
From $E=mc^{2}$ we know that energy is related to mass.
This means that we can calculate how much energy is released in a process if we measure the mass before and after.
The difference in mass is called _mass defect_
### Example:
$4 \cdot H \to He$
$m_{H}= 1.00784 u$
$4m_{H}= 4.03136u$
$m_{He}= 4.002602 u$
$\Delta m = 4 m_{H}-m_{He}= 0.028758 u = 4.78\cdot 10^{-29} kg$
$\Delta E = \Delta m c^{2} = 4.29\cdot 10^{-12} J$
Note the same also works in reverse when $U \to Fe$
## Energy structure
In the previous chapters we saw that the type of light (i.e. it's wavelength) is related to the energy of an individual photon.
$E_{photon}= \frac{hc}{\lambda}$
Due to quantum mechanical reasons electrons in atoms are confined to specific energy levels.
If we want to interact with those electrons we need to give them the correct amount of energy to transfer between two of those energy levels.
Those energy levels are often labeled in units of eV (electron volts)
$1eV = 1.60 \cdot 10^{-19}J$
$1eV = \frac{1239.8}{\lambda (nm)}$
Source: https://astro.unl.edu/naap/hydrogen/transitions.html
### Hydrogen like atoms:
$E(n) = \frac{R_{\infty}ch Z^{2}}{n^{2}}$
$R_{\infty}$: Rydberg constant $1.097 \cdot 10^{7} m^{-1}$
$Z$: Charge of core (1 for $H^{+}$)
$n$: The energy level
Now we know that $hf = \frac{hc}{\lambda} =^{!} \Delta E$
$\frac{1}{\lambda}= R_{\infty} Z^{2} (\frac{1}{n_{1}^{2}}- \frac{1}{n_{2}^{2}})$
__image couldn't be loaded__
These series are also experimentally visible:
# Heat
## Equilibrium
System tend to equilibrium, meaning that there is no imbalance left.
Ex.
- Putting a hot and a cool object in a room will lead to two medium warm objects.
- Putting helium in the left half of a room and hydrogen in the right half will lead to two halfs of the room both filled 50:50 by He and H
- etc
Exam tip:
- If you do not know why something happens
- -> Guess because of thermodynamics
- Why do black holes evaporate over time?
- -> Thermodynamics
- -> There needs to be involvement of heat -> heat -> blackbody radiation -> black holes need to radiate something -> hawking radiation!
## Gas
A gas is a collection of very looseley bound atoms/molecules. They are well described by
- Pressure $p$
- Volume $V$
- Number of particles: $n$
- Temperature $T$
These properties relate to eachother via the _Ideal gas law_:
$pV = nRT$
with $R=8.314 \frac{J}{K mol}$ the molar gas constant
### Intuition:
for $n,T$ const. (isothermal)
$p \uparrow \to V \downarrow$
for $n,V$ const (isochor)
$p \uparrow \to T \uparrow$
for $n, p$ const (isobar)
$V\uparrow \to T \uparrow$
## Entropy (bonus)
Entropy relates extractable heat to temperature.
$dS = \frac{dQ_{rev}}{T}$
Meaning the change in entropy is the change of heat at a specific temperature.
A completeley different approach to entropy is the number of 'equally labeled' states.
$S = k_{B} \ln \Omega$
Meaning that if I can give every single state a label $\Omega$ is small -> small entropy
If many states have the same label $\Omega$ is large -> high entropy
Ex.
- If I tell you my room is tidy. You know that there are not many states of the room I would call tidy. Ie $\Omega$ is small -> low entropy
- If I tell you my room is messy. There are a billion different ways my room can be messy. All of those different types of messy rooms are labeled as 'messy' ie $\Omega$ is large -> high entropy
### Relation
How do those two forms of entropy relate to eachother?
The intuition is: It's easier to clean a almost tidy room than it is to clean a room which is messy.