Thermodynamics of Black-Body Radiation

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


Problem 4

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


Problem 5

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 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?


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?