Thermodynamics of Black-Body Radiation

From Universe in Problems
Revision as of 11:39, 15 October 2012 by Igor (Talk | contribs)

Jump to: navigation, search

Problem 1: chemical potential

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


In the next 4 problems we consider some volume $V$, filled with black-body radiation of temperature $T$.

Problem 2: number density distribution

Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$.


Problem 3 total number

Find the total number of photons.


Problem 4: gas oven

What is this number for a gas oven at room temperature and at maximum heat?


Problem 5: energy distribution

What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$?


Problem 6: thermodynamic potentials

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


Problem 7: thermal capacity

Calculate the thermal capacity of black-body radiation.


Problem 8: pressure

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


Problem 9: adiabatic equation

Find the adiabatic equation for the black-body radiation.


Problem 10: CMB as microwave

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


Problem 11: Planck distribution

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?