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The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
[5] In fact, if the ground-state energy behaves proportional to for some , then pouring two glasses of water would provide an energy proportional to () = (), which is enormous for large . A system is called stable of the second kind or thermodynamically stable when the free energy is bounded from below by a linear function of N {\displaystyle N} .
A simplified phase diagram for water, showing whether solid ice, liquid water, or gaseous water vapor is the most stable at different combinations of temperature and pressure In physics , a state of matter is one of the distinct forms in which matter can exist.
Electrons in metals also behave as if they were free. In reality the particles that are commonly termed electrons in metals and other solids are quasi-electrons—quasiparticles, which have the same electrical charge, spin, and magnetic moment as real electrons but might have a different mass. [134]
Electrons are affected by two thermodynamic forces [from the charge, ∇(E F /e c) where E F is the Fermi level and e c is the electron charge and temperature gradient, ∇(1/T)] because they carry both charge and thermal energy, and thus electric current j e and heat flow q are described with the thermoelectric tensors (A ee, A et, A te, and A ...
This pressure is called the electron degeneracy pressure and does not come from repulsion or motion of the electrons but from the restriction that no more than two electrons (due to the two values of spin) can occupy the same energy level. This pressure defines the compressibility or bulk modulus of the metal [Ashcroft & Mermin 8]
For example, liquid helium does not freeze under atmospheric pressure regardless of temperature due to its zero-point energy. Given the equivalence of mass and energy expressed by Albert Einstein 's E = mc 2 , any point in space that contains energy can be thought of as having mass to create particles.
If many electrons are confined to a small volume, on average the electrons have a large kinetic energy, and a large pressure is exerted. [ 2 ] [ 3 ] : 32–39 In white dwarf stars, the positive nuclei are completely ionized – disassociated from the electrons – and closely packed – a million times more dense than the Sun.