HW #5 - Prof. Jennifer Curtis School of Physics, Georgia...

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1 Prof. Jennifer Curtis School of Physics, Georgia Tech Spring 2012 Statistical Mechanics 4142: Problem Set 5 Due : Friday, February 17, 2012 [1] Thermal Energy Scales. We’ve noted in class that the fundamental temperature, τ , has the same dimensions as energy, E , and that for a system with an unbounded spectrum of energies, like a quantum oscillator, the mean energy τ in the high-temperature limit. You will soon explore the equipartition theorem, which again will relate mean energy to τ . One often uses energy and temperature “interchangeably,” referring to the temperature that corresponds to a particular energy, via the relations τ E and τ = k B T , where T is the conventional temperature and Boltzmann’s constant Joules/Kelvin. Here are some short questions on “characteristic” temperatures. (a) (1 pt) A characteristic energy scale for removing electrons from atoms is ~1 eV; 1 eV is the energy of 1 electron (charge 1.6 × 10 - 19 Coulombs) in a 1 Volt potential. The universe used to be very hot, and has been cooling while expanding since the Big Bang. Free protons and electrons scatter light very effectively compared to bound atoms; the universe became relatively transparent to thermally generated photons when stable atoms could exist, which occurred about 13.7 billion years ago, 400,000 years after the big bang. What was the temperature of the universe at this point? (Light from this period is what one sees in the cosmic microwave
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HW #5 - Prof. Jennifer Curtis School of Physics, Georgia...

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