only part a 5: Thermometry, the sun, and exotic particles (8 points) (a) (4 poin
ID: 1377004 • Letter: O
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only part a
5: Thermometry, the sun, and exotic particles (8 points) (a) (4 points) Find the derivative of pT(v) with respect to v (or 1w, whichever you find easier to do the algebra for), set that derivative equal to zero, and simplify the resulting equation as much as you can. (Don?t worry, I don?t expect you to solve it by hand.) (b) (2 points) Solve that equation graphically to find the energy that maximizes pT(v). You can use a graphing calculator, Mathematica. Matlab, or whatever else you want to use. It might help if you simplify the algebra by plotting the derivative as a function of x E/kT. Everything depends on that ratio. so solve for that ratio. Once you have the ratio of E to kT, solving for E is really, really easy. (c) Researchers at the Cern Axion Solar Telescope (CAST) are trying to detect a hypothetical particle called the axion. Axions are hypothesized to form in the center of the sun when an x-ray converts into a photon in the presence of intense electric and magnetic fields. The energy of the axion is equal to the energy of the x-ray that formed it. If CAST researchers are looking for axions with an energy spectrum that peaks around 1 keV, what is the temperature in the center of the sun?Explanation / Answer
Thermometry is the science and practice of temperature measurement. Any measurable change in a thermometric probe (e.g. the dilatation of a liquid in a capillary tube, variation of electrical resistance of a conductor, of refractive index of a transparent material, and so on) can be used to mark temperature levels, that should later be calibrated against an internationally agreed unit if the measure is to be related to other thermodynamic variables (if the measure is only needed to establish an ordering in thermal levels, no calibration is required).
Coulomb blockade is destroyed for large thermal energies Condition for thermally activated electron transfers
: e 2 8C ? kBT
Resistance Re has to be sufficiently large for single electron tunneling eRe/ V h/ eV ? Re
h /e 2 = 25.81 k?
t: Applied voltage leads to oscillations in curren
t d?/ dt = 2e ~ V
? = 2eV ~ f = 2eV h
Josphson constant: 2e h ' 4.84
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