Difference between revisions of "Thermodynamics of Black-Body Radiation"

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[[Category:Cosmic Microwave Background (CMB)|1]]
 
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<div style="border: 1px solid #AAA; padding:5px;">
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=== Problem 1 ===
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Show that the photon gas in thermal equilibrium has zero chemical potential.
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=== Problem 1 ===
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Find number of photons in black-body radiation of temperature $T$ in volume $V$, which have frequencies in the interval $\left[ \omega ,\omega +d\omega  \right]$.
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  <div class="NavHead">solution</div>
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=== Problem 1 ===
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Find total photon number of black body radiation in volume $V$ at temperature $T$.
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=== Problem 1 ===
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Estimate number of photons in a gas oven at room temperature and at maximum heat.
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  <div class="NavHead">solution</div>
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=== Problem 1 ===
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Find energy of photons in black-body radiation of temperature $T$ in volume $V$, which have frequencies in the interval $\left[ \omega ,\omega +d\omega  \right]$.
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  <div class="NavHead">solution</div>
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=== Problem 1 ===
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Calculate free energy, entropy and total energy of black-body radiation.
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=== Problem 1 ===
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Calculate thermal capacity of black-body radiation.
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=== Problem 1 ===
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Find pressure of black-body radiation and construct its state equation.
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=== Problem 1 ===
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Find adiabate equation for the photon gas of black-body radiation.
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=== Problem 1 ===
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Why CMB cannot be used to warm up food like in the microwave oven?
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    <p style="text-align: left;">The relic radiation, or CMB, corresponds to the black-body radiation with temperature $T_{CMB}=2.725\:K.$
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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 $T_{CMB}.$</p>
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=== Problem 1 ===
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The binding energy of electron in the hydrogen atom equals to $13.6\
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eV$. What is the temperature of Planck distribution, with this
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average photon energy?
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    <p style="text-align: left;">The Planck distribution has maximum at frequency $\omega_m = 2.822 kT/\hbar.$ Then one obtains
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$ kT = 13.6/2.822 = 4.82\mbox{eV}$ and $T\approx 5.6 \cdot {10^4}\mbox{K}$.</p>
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</div></div>

Revision as of 19:26, 30 September 2012



Problem 1

Show that the photon gas in thermal equilibrium has zero chemical potential.


Problem 1

Find number of photons in black-body radiation of temperature $T$ in volume $V$, which have frequencies in the interval $\left[ \omega ,\omega +d\omega \right]$.


Problem 1

Find total photon number of black body radiation in volume $V$ at temperature $T$.


Problem 1

Estimate number of photons in a gas oven at room temperature and at maximum heat.


Problem 1

Find energy of photons in black-body radiation of temperature $T$ in volume $V$, which have frequencies in the interval $\left[ \omega ,\omega +d\omega \right]$.


Problem 1

Calculate free energy, entropy and total energy of black-body radiation.


Problem 1

Calculate thermal capacity of black-body radiation.


Problem 1

Find pressure of black-body radiation and construct its state equation.


Problem 1

Find adiabate equation for the photon gas of black-body radiation.


Problem 1

Why CMB cannot be used to warm up food like in the microwave oven?


Problem 1

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?