User:PAR



Subjects I'm working on


 * Writing better articles
 * Help:Wikitext
 * Help:Displaying_a_formula



Help:Displaying a formula

$$dU=\underbrace{\delta Q}_{\delta Q} + \underbrace{\delta W_{irr}+\delta W_{rev}}_{\delta W}$$

$$dU=\underbrace{\delta Q + \delta W_{irr}}_{T\,dS}+\underbrace{\delta W_{rev}}_{-P\,dV}$$

==References== === Bibliography === *
 * References
 * References, , ,
 * References (Harvard with pages)


 * Template:Cite_web
 * Template:Cite_journal
 * Template:cite book


 * 1) History of Wayne, NY
 * 2) Australian Trilobite Jump table
 * 3) RGB
 * 4) -
 * 5) Pigment-loss color blindness
 * 6) Peach
 * 7) Work7
 * 8) Work8
 * 9) Extension to Kummer's test
 * 10) Work10
 * 11) Elastic Moduli
 * 12) Work 12


 * equivlist


 * Principle of maximum entropy
 * Principle of maximum work
 * Principle of minimum energy
 * Minimum total potential energy principle


 * Template talk:probability distribution
 * Template talk:Prettytable and MediaWiki talk:Common.css
 * verify &mu; is mode of Levy distribution
 * Combine Heavy tail distribution and Long tail
 * Mutation-selection balance | Quasispecies model | http://www.biomedcentral.com/1471-2148/5/44

Thermodynamics

 * Thermodynamic Equations
 * Laws of thermodynamics
 * Ideal gas
 * Sackur-Tetrode equation
 * Gibbs paradox

Heavy tail distributions
Heavy tail distributions

Statistical Mechanics
Others:
 * Entropy
 * Principle of maximum entropy

Continuum mechanics

 * Boltzmann equation
 * Navier-Stokes equations
 * Fluid mechanics


 * http://online.physics.uiuc.edu/courses/phys598OS/fall04/lectures/

Work pages
To fix:
 * Degenerate distribution
 * Fermi-Dirac statistics - not continuous, necessarily
 * Bose gas (derive critical temperature)
 * Spectral density-SPD Cat:Physics = Power spectrum-Cat:signal processing

 Proof: Introduce an additional heat reservoir at an arbitrary temperature T0, as well as N cycles with the following property: the j-th such cycle operates between the T0 reservoir and the Tj reservoir, transferring energy dQj to the latter. From the above definition of temperature, the energy extracted from the T0 reservoir by the j-th cycle is


 * $$dQ_{0,j} = T_0 \frac{dQ_j}{T_j} \,\!$$

Now consider one cycle of the heat engine, accompanied by one cycle of each of the smaller cycles. At the end of this process, each of the N reservoirs have zero net energy loss (since the energy extracted by the engine is replaced by the smaller cycles), and the heat engine has done an amount of work equal to the energy extracted from the T0 reservoir,


 * $$W = \sum_{j=1}^N dQ_{0,j} = T_0 \sum_{j=1}^N \frac{dQ_j}{T_j} \,\!$$

If this quantity is positive, this process would be a perpetual motion machine of the second kind, which is impossible. Thus,


 * $$\sum_{i=1}^N \frac{dQ_i}{T_i} \le 0 \,\!$$

Now repeat the above argument for the reverse cycle. The result is


 * $$\sum_{i=1}^N \frac{dQ_i}{T_i} = 0 \,\!$$ (reversible cycles)

In mathematics, it is often desireable to express a functional relationship $$f(x)\,$$ as a different function, whose argument is the derivative of f, rather than x. If we let y=df/dx be the argument of this new function, then this new function is written $$f^\star(y)\,$$ and is called the Legendre transform of the original function.


 * Random variable
 * Random sequence
 * Random number
 * Pseudorandom number generator
 * STOCHASTIC PROCESS
 * Time series
 * Stationary process
 * Category:Random numbers
 * Category:Stochastic processes
 * Category:Noise
 * Category:Statistics
 * Category:Probability theory

References

δQh is heat, δWx is irreversible work, so TdS=δQh+δWx. If both are zero, then dS=0. For the 3 possible walls, "T ins" means thermally insulated, and "No IW" means no irreversible work. "External" specifies the region external to the system.