E.5 The entropy conceptEdit
Carnot first developed the concept of entropy in his work on heat engines. By building a theoretical model of an engine which achieved 100% efficiency, he was, in fact, assuming that entropy could be made constant, as everything in this model was being done reversibly.
Clausius and Kelvin also worked on the macroscopic interpretations of entropy (Clausius coined the term).
Boltzmann developed the microscopic interpretation, based on the random motion of particles.
Clausius used entropy to describe the degradation, and unavailability of energy. Even though energy is conserved, it is only useful if it can be made to do something. For example, a system where one area is hot, while the other is cold is more useful than a system with the same amount of heat, but distributed evenly. When energy is spreads out more evenly, it is said to be degraded.
Maxwell's daemon is a 'thought experiment' which tries to overcome the law that entropy must always increase. We imagine that there are two containers filled with gases, connected by a small pipe. In the centre is a daemon, and, as daemons do, it wants to try to increase the temperature in one side, and decrease that in the other, thus defying the law of entropy. He/she/it does this by opening and closing a door, allowing fast moving particles to go through into the left, and slow moving particles into the right. This separation of fast and slow moving particles means entropy is being defied.
The problem with this is that for the demon to be doing this, energy must be used, so even if the entropy inside is decreasing, the energy to achieve this will be greater, and so there will be a larger increase in entropy somewhere else.
When analyzing systems in thermodynamic terms, it is important to consider both the first and second laws. Both the quantity of energy, and the quality must be considered to understand the usefulness and ability of the system to do work.
E.6 The quantum conceptEdit
The cavity radiator oscillator (aka black body radiator) relates to objects which absorb all the electromagnetic energy which strikes them. As the wavelength of the radiation decreases ( i.e. increased frequency ) the oscillations of the particles in the object increase. It therefore stands to reason that, eventually, the oscillations would become so large that the radiator would simply fall apart. This wavelength was calculated to be within the ultraviolet spectrum, hence the name ultraviolet catastrophe.
Max plank's idea was that energy could only be absorbed or emitted by radiators in discrete amounts, and so a low frequency is less likely to give energy to a high frequency oscillator because the energy emitted by such a low frequency oscillator would not be of sufficient energy. Thus, the ultraviolet catastrophe does not occur.
E.7 Conservation principles and symmetryEdit
The four fundamental forces are:
Gravity : Long range, very weak compared to the others.
Electromagnetic : Long range, stronger, but only significant at small distances.
Weak : Short range, and stronger than gravity, weaker than electromagnetic.
Strong : Very short range (only affects the nearest nucleons), and very strong.
The fundamental particles known in 1935 were protons, neutrons and electrons.
The strong force acts to hold the nucleus together.
The weak force is involved in the transformation of neutrons into protons by beta decay.
The model used for the movement of forces is that of a 'virtual exchange' particle. Each of the 4 forces has an associated virtual particle (though the graviton's existence has never been proved).
- Strong force : gluons (formerly mesons, which is what the syllabus says)
- Electromagnetic force : Photon
- Weak nuclear force : Bozon
- Gravity : Graviton
A feynman diagram basically shows the two particles Moving towards each other, then moving away, with a dotted line between the turning point representing the movement of the virtual particle.
Things that are conserved in nuclear reactions :
- Angular momentum
- Electric charge
- Lepton number
- Muon number
- Baryon number
These should all be considered when nuclear reactions are being written (but the momentum ones can't really be written).
A symmetry operation (thank god for abstract algebra) is an 'operation' which involves a rotation or translation in which everything is conserved.
Murray Gell-Mann's 'eightfold way' was a model based on the SU3 group which was designed to model the particles which quarks composed. It was used to predict the existence of the Omiga minus particle, and the properties thereof before it was physically found.
There are six quarks : up, down, strange, charmed, top (aka truth) and bottom (aka beauty). In addition to these, each has its own antiquark, with opposite charge, and opposite strangeness, charm, topness or bottomness as appropriate. They also have a baryon number of -1/3 as opposed to 1/3 for the normal quarks.
These quarks are composed together to form the different particles. They each have charges of ±1/3 or ±2/3, and get stuck together to form particles like the proton (uud) and neutron (udd). Up quarks have a charge of +2/3, down quarks have a charge of -1/3 (note that the other types are not as common).
Quarks also have a quality called color with possible values of red, blue, green, anti-red, anti-blue and anti-green.
The idea was originally proposed to preserve the Pauli exclusion principle. The quarks are held together by the exchange of particles called gluons (which is sort of like the strong force). There are 8 gulons, 6 of which have a color charge.
Organizational principles in science : They're good, and help to, well, organise things. They help to show trends in data which otherwise is just a mess.
Examples are the eightfold way, and the unification of the forces.