Difference between revisions of "Thermodynamics of Black-Body Radiation"
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=== Problem 6 === | === Problem 6 === | ||
Calculate free energy, entropy and total energy of black-body radiation. | Calculate free energy, entropy and total energy of black-body radiation. | ||
Revision as of 11:31, 15 October 2012
Problem 1
Show that the photon gas in thermal equilibrium has zero chemical potential.
Problem 2
Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$ in a volume $V$ filled with black-body radiation of temperature $T$.
Problem 3
Find total number of photons in the volume $V$ filled with black body radiation at temperature $T$.
Problem 4
Estimate the number of photons in a gas oven at room temperature and at maximum heat.
Problem 5
What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$, filling the volume $V$ at temperature $T$?
Problem 6
Calculate free energy, entropy and total energy of black-body radiation.
Problem 7
Calculate thermal capacity of black-body radiation.
Problem 8
Find pressure of black-body radiation and construct its state equation.
Problem 9
Find adiabate equation for the photon gas of black-body radiation.
Problem 10
Why CMB cannot be used to warm up food like in the microwave oven?
The relic radiation, or CMB, corresponds to the black-body radiation with temperature $T_{CMB}=2.725\:K.$ According to the main principle of thermodynamics, heat cannot transfer from a less heated body to more heated one, and thus the body (food in our case), which initially had temperature $T_0>T_{CMB},$ will emit more energy in the environment then absorb back, until the equilibrium installs with the CMB radiation at temperature $T_{CMB}.$
Problem 11
The binding energy of electron in the hydrogen atom equals to $13.6\ eV$. What is the temperature of Planck distribution, with this average photon energy?
The Planck distribution has maximum at frequency $\omega_m = 2.822 kT/\hbar.$ Then one obtains $ kT = 13.6/2.822 = 4.82\mbox{eV}$ and $T\approx 5.6 \cdot {10^4}\mbox{K}$.
