Thermodynamics.
"The combined studies of heat, work, and temperature and their relation to energy, entropy, and the physical properties of matter and radiation."
Table of contents:
1. Laying Down the Law.
2. (Incredibly) Cool Cucumbers.
3. Systems.
4. Time Flies.
4. Maddening Behaviour.
1. Laying down the Law.
At the very core of thermodynamics, there are three laws that describe how energy flows in certain directions and in certain ways. All the interesting energy calculations are based on these laws so its very important we understand them:
1. "Energy can neither be created or destroyed."
The total energy of the universe is a constant - from the big bang to the present day. You cannot destroy energy but you can convert it between stores (these could be kinetic, thermal, nuclear, chemical or gravitational potential energy). In the rest of this chapter we will talk of energy transfers within systems - always remember we are never creating or destroying energy but just reshuffling it into a different store.
An interesting aside here: the first law of thermodynamics does not hold true over ludicrously small time frames. Virtual particles (see the quantum physics chapter) can violate it but only for a very small amount of energy which exists for a very small length of time.
2. "Both the total entropy of a system and of the universe increases for a spontaneous process."
Entropy has been described as the worst explained and understood idea in all of physics. Entropy is the measure of disorder or uncertainty in a system. It can be thought of through the analogy of a car:
Before it starts moving, the car has very low entropy, all the energy in the car is in an ordered state: it is contained in chemical potential energy of the fuel, gravitational potential energy and mass-energy of the matter contained in the car.
However, once the car starts moving, it's energy becomes much more disorganised. Lots of energy is directly converted into kinetic energy. Some is converted into gravitational potential energy if the car rises and some is lost to waste sources such as heat and noise in the engine.
Another example would be a box of coloured crayons. If they are organised into rows by colour, we say the entropy is low as the system has definite order. If however, a messy child comes along and shuffles the crayons around, the system gains entropy as disorder has been introduced.
Now in a disordered state, if the messy child remixes them, there remains a very small chance that the crayons will return to their original state. It is much more likely that they become even more disordered though.
Entropy is therefore a practical application of probability - the system is more likely to become further disordered than it is return to an ordered state.
Returning to the analogy of the car, there are an undefinably large number of individual atoms, each with individual energy characteristics, involved in the system. It is therefore so unlikely the atoms return to their original ordered state we can say that it never happens and that whenever an energy-transfer process occurs, entropy always increases.
3. "A perfect crystal at 0 Kelvin has 0 entropy. When heated, all objects gain entropy.“
Temperature is a measure of thermal energy in an object. Thermal energy is the energy stored in the vibration and movement of the particles inside it. As the object heats up, the particles inside it vibrate faster and further from their position of equilibrium.
To decode this law: 0 Kelvin is -273 Celsius and is known as absolute zero - it is the coldest possible temperature in the universe because at 0K the particles have zero thermal energy and so are stationary.
A perfect crystal is a crystal with a uniform lattice made of only one type of particle. It also has no defects (the lattice is perfectly uniform).
Both of these requirements can never be practically achieved in the real world:
Achieving Absolute Zero?
There are two ways to explain why an object can never reach absolute zero:
Classical mechanics - In order to make an object colder than it currently is, it needs to be placed near an object or in a system that is colder than it. This is so thermal energy can transfer from the object to it's surroundings.
Therefore, it is impossible to cool an object down to absolute zero as you would need an object that is colder than absolute zero to squeeze out the last bit of thermal energy.
Quantum mechanics - All particles vibrate on a quantum level and so we can never go below the temperature a particle has due to it's own quantum vibration.
Achieving a Perfect Crystal?
A perfect crystal is one with no point, line or planar defects. This is a very fancy way of saying no bumps or creases in the lattice.
Crystals formed naturally in the earth, are always made up of lots of smaller crystals pressed together under immense heat and pressure. This process of combining smaller crystals always causes small defects - known as grain defects.
Lab-grown crystals suffer less from this type of defect but are still prone to another: known as stacking faults. This occurs for crystals made of molecules with internal symmetry - such as octagonal ones.
Stacking faults occur when one octagonal shape is rotated many times throughout the crystal. Even if each atom lines up, the 8 vertical lines of individual atoms this forms may not be symmetrical to each other and so the crystal is not perfect.
2. (Incredibly ) Cool Cucumbers.
Although we can never reach absolute zero, we can get very very close by using lasers. This sounds strange and counter-intuitive as we often associate lasers with being hot and burning through things. Claude Cohen-Tannoudji, Steven Chu, and William Daniel Phillips were awarded the 1997 Nobel Physics prize for experimentally achieving laser cooling.
Laser Cooling.
When a photon is absorbed by an atom, it causes an electron orbiting in a lower shell of that atom to become excited. Depending on the frequency of the incident light beam, this electron is either excited to a higher energy shell or ionised away from the atom.
If the electron is not ionised, and merely orbits in a higher shell, it will want to return to its lower orbit. This process is an extension of the idea of least energy; the electron 'chooses' to orbit closer to the nucleus because it is in a lower energy state.
![electron-photon emission]](https://duyn491kcolsw.cloudfront.net/files/1j/1jk/1jkuy6.jpg?ph=b51fa12eef)
There are two ways for an electron to de-excite its way down the orbital shells to return to the lowest-energy unoccupied shell:
- It can emit a second photon with an identical frequency, wavelength and energy as the one it absorbed. This causes it to move down multiple shells in one jump.
- It can emit multiple photons, each with a lower frequency than the one it absorbed and so drop down through intermediately shells - releasing corresponding photons for each jump as seen to the left.
As a science, physics builds upon a set of unalterable laws, one of which is the conservation of momentum which says:
"The total momentum of a closed system before a collision/explosion must equal the total momentum of the system afterwards."
Picture the atom as a beach ball and the incident photons as a stream of flying peas. If the peas collide with the stationary beach ball and stick to it, the beach ball rolls forwards as it needs to conserve the momentum of the system.
Now picture what would happen if the beach ball held onto the peas momentarily before shooting them back in the direction they came from. This would further increase the speed of the ball's rolling - following the same principle that causes rockets to accelerate when they fire ignited fuel behind them.
We can therefore take an atom and fire a photon at it. When it absorbs the photon (remember photons have momentum even though they do not have mass - see special relativity chapter) it is pushed in the direction the photon was traveling.
The photon also causes an electron in the atom to excite momentarily and the resulting emission of the photon (or several smaller photons) when the electron de-excites acts as a secondary push. However, the emitted photon is released in a random direction.
Lets examine the two extreme cases for the direction of the emitted photon:
- The photon is emitted in the same direction as the exciting photon. Because the total energies of the emitting and absorbing photons are always identical, if the atom fires a photon back in the direction of the oncoming exciting photon, it essentially cancels out the push given to it by the ionising photon. The overall movement of the atom after this process is therefore 0. This is seen in the first line on the left.
- The photon is emitted in the opposite direction as the exciting photon. This is like the beach ball (from our earlier analogy) spitting out the peas back in the direction they came from. This gives the atom a second 'push' in the same direction and so the overall movement is 2 photons-worth-of-push in the direction of the exciting photon as seen in the middle left.
As these are the two extreme cases, for all other directions of photon emission the overall movement must be between 0 and 2 photons-worth-of-push in the direction of the exciting photon. These come from the intermediate angles of emission seen on line three above.
A laser beam is nothing more or less than a focused stream of photons. So when the laser hits the atoms in the cloud of gas, every single photon causes the atoms to move (depending on the angle of emission) a certain distance.
How does causing the atom to move help with cooling it down? Surely by moving it you increase it's temperature!
Temperature is a measure of how much the average particle in an object vibrates. To cool a particle to almost absolute zero, you need to minimise the amount of movement it has - although due to quantum vibrations you can never make this movement zero.
Laser cooling works by placing 6 incident beams of light (lasers) on the sample that is to be supercooled. These beams are fired from the surfaces of a cube placed around the sample such that each axis in 3 dimensional space has two lasers (acting in opposite directions) firing through it.
This experimental set up is shown to the right:
Laser cooling of a gas cloud relies on a very simple principle: you can't beat probability.
As the 6 incident beams of light shine through the cloud of gas, any given particle found inside the cloud is more likely to interact with a photon that is traveling in the opposite direction to it's own motion. This is due to the doppler effect:
The Doppler Effect.
The doppler effect is a phenomena of waves being emitted from a moving object. Consider the sound an f1 car makes as it drives by a stationary observer. The noise of it's engine goes from high to low pitch as it moves past.
This is because as it moves forward, any sound waves being emitted by the car in the direction of travel move slower relative to the car than those being emitted against the direction of travel.
The practical application of this is that even though the frequency of the sound remains a constant in all directions, the wavelength of the sound appears to be shorter in front and longer behind the car.
IMPORTANT NOTE: due to the joy of relativity, only the stationary observer views the sound waves being distorted in this manner. To the driver (who moves with the waves), there is no change to wavelength.
The apparent shortening and lengthening wavelength of the sound wave explains the differing noises heard by the observer as the car moves past them. The faster the car moves, the greater the difference in wavelength (and so pitch of note) is seen.
If the car were to break the speed of sound (330m/s), the waves would be moving slower than it and so the stationary observer would not hear the car until it had passed them. In many ways then, the doppler effect for sound waves is a less-extreme case of the sonic boom heard when breaking the speed of sound.
Doppler Effect when Moving Atoms in Laser Cooling.
The Doppler Effect applies to all types of waves - including light waves. In laser supercooling, the 6 beams of light fired into the gas cloud have very specific frequency which is slightly below the required frequency (and therefore energy) needed to excite an electron. If all the particles of gas were completely stationary then the beams of light would just fly straight through and not be absorbed.
However this is not the case as the particles in the cloud are constantly in motion. Particles that move in the same direction as a give beam of light, perceive that light to be 'red-shifted'. This is the name given to the components of the beam that have their wavelength increased (and so are closer to the red end of the spectrum).
As they pecieve the wavelength of the light to be increased, the frequnecy of the light must also be decreased as seen in the proportional equation v = f λ.
Therefore, particles moving in the same direction as the incident light do not absorb it as the frequnecy of the light is too low to cause electron excitement.
The opposite is true for particles that move against the incident light. These particles perceive the beams of light to be 'blue-shifted'.
As the frequency of the light is slightly below the level needed to excite atoms, when the light's frequency is increased by the doppler effect for atoms moving in the opposite direction, the atoms can absorb the photons as the frequency matches.
3. Systems.
The problem with thermodynamics in the wider world is it becomes far too complicated. It would be impossible to fully analyse all the particles and entropy in a given space because it will always be influenced by the movement of energy outside the space. To simplify this, we use Thermodynamic Systems:
Thermodynamic System - a body of matter and/or radiation separate from its surroundings that can be independently studied using the laws of thermodynamics.
This makes systems incredibly useful because by simplifying a space into system, a very good model of it's energy interactions can be produced.
There are two main types of system:
Passive Systems.
The idea of thermal energy being transferred around a system has a very interesting cosmological application:
The Heat Death of the Universe.
Many physicists believe that the universe, in contrast to the exciting big bang, will have an incredibly boring end. By combining the idea of a passive system and the second law of thermodynamics, we can predict that as time goes on, the heat energy in the universe will become more and more dispersed.
In the same way a block of ice melts in a warm bath (causing a universal temperature), as time goes on the passive system relating to heat that encompasses the whole universe will tend towards equilibrium.
The heat death of the universe is the idea that at some point all matter will be the same temperature and entropy will reach a maximum (Smax). Once this has happened, the universe is officially energy-dead as there is no longer any potential for work to be done in any capacity.
Active System.
Interacting Systems.
Isolated System.
Isolated systems do not exchange matter or energy with their surroundings. An isolated system acts as it's own microclimate and as discussed earlier is not achievable in real life but serves a simplification for more complex systems.
Closed System.
Closed systems do not exchange matter but can exchange energy. This means that particles can not exit the system but energy (usually in the form of heat) can.
Open system.
Both energy and matter can be exchanged in an open system. This is the most realistic model of the energy transfers in real life. However, it becomes incredibly complex as matter and radiation from distant parts of the universe affect the system. This idea of never knowing enough about the energy transfers occurring outside the system is pivotal to a mathematical model we will meet later on called Chaos Theory.
4. Time Flies.
As stated by the second law of thermodynamics, the entropy of all systems is always increasing. This simply means that as time goes on, the total energy of the system becomes less ordered and there is a greater uncertainty in it's position.
The entropy of a system always increases as time goes on. We can therefore define the direction of time as the direction of increasing entropy .