Difference between revisions of "Thermodynamics of Black-Body Radiation"
| Line 9: | Line 9: | ||
Show that the photon gas in thermal equilibrium has zero chemical potential. | Show that the photon gas in thermal equilibrium has zero chemical potential. | ||
<div class="NavFrame collapsed"> | <div class="NavFrame collapsed"> | ||
| − | <div class="NavHead"> | + | <div class="NavHead">solution</div> |
<div style="width:100%;" class="NavContent"> | <div style="width:100%;" class="NavContent"> | ||
<p style="text-align: left;"></p> | <p style="text-align: left;"></p> | ||
Revision as of 20:07, 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?
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 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?
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 $T\approx 5.6 \cdot {10^4}\mbox{K}$.
