Difference between revisions of "Thermodynamics of Black-Body Radiation"
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| + | Now let us consider in the next 4 problems some volume $V$, filled with black-body radiation of temperature $T$. | ||
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=== Problem 2 === | === Problem 2 === | ||
| − | Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega] | + | Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$. |
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=== Problem 3 === | === Problem 3 === | ||
| − | Find total number of photons | + | Find the total number of photons. |
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=== Problem 4 === | === Problem 4 === | ||
| − | + | What is this number for a gas oven at room temperature and at maximum heat? | |
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=== Problem 5 === | === Problem 5 === | ||
| − | What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega] | + | What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$? |
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=== Problem 6 === | === Problem 6 === | ||
| − | Calculate free energy, entropy and total energy of black-body radiation. | + | Calculate the free energy, entropy and total energy of black-body radiation. |
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=== Problem 7 === | === Problem 7 === | ||
| − | Calculate thermal capacity of black-body radiation. | + | Calculate the thermal capacity of black-body radiation. |
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=== Problem 8 === | === Problem 8 === | ||
| − | Find pressure of black-body radiation and construct its state equation. | + | Find the pressure of black-body radiation and construct its state equation. |
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=== Problem 9 === | === Problem 9 === | ||
| − | Find | + | Find the adiabatic equation for the black-body radiation. |
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=== Problem 11 === | === Problem 11 === | ||
The binding energy of electron in the hydrogen atom equals to $13.6\ | The binding energy of electron in the hydrogen atom equals to $13.6\ | ||
| − | eV$. What is the temperature of Planck distribution | + | eV$. What is the temperature of the Planck distribution with this |
average photon energy? | average photon energy? | ||
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Revision as of 11:36, 15 October 2012
Problem 1
Show that the photon gas in thermal equilibrium has zero chemical potential.
Now let us consider in the next 4 problems some volume $V$, filled with black-body radiation of temperature $T$.
Problem 2
Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$.
Problem 3
Find the total number of photons.
Problem 4
What is this number for a gas oven at room temperature and at maximum heat?
Problem 5
What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$?
Problem 6
Calculate the free energy, entropy and total energy of black-body radiation.
Problem 7
Calculate the thermal capacity of black-body radiation.
Problem 8
Find the pressure of black-body radiation and construct its state equation.
Problem 9
Find the adiabatic equation for the 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 the 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 $T\approx 5.6 \cdot {10^4}\mbox{K}$.
