Photon Gas
#Physics
Topics
$\displaystyle {\left\langle{\varepsilon}\right\rangle}={\left\langle{s}\right\rangle}\hbar \omega$
- $\displaystyle \varepsilon$ is the average energy for the frequency mode $\displaystyle \omega$
- $\displaystyle {\left\langle{s}\right\rangle}$ can be found by the Planck distribution function
$\displaystyle {\left\langle{\varepsilon}\right\rangle}=\hbar {\omega}_{0}\left( {\left\langle{s}\right\rangle}+\frac{1}{2} \right)=\frac{1}{2}\coth\left(\frac{\hbar\omega}{\tau} \right)$
- Expanded version of above...
$\displaystyle H=pc=\hbar kc=\hbar c\left( \frac{\pi}{L}\sqrt{ n_{x}^{2}+n_{y}^{2}+n_{z}^{2} } \right)$
- The energy of a photon gas in a cavity
$\displaystyle U=-\sum_{n}s_{n}\hbar \omega_{n}$
- Internal energy of a photon gas
- $\displaystyle s_{n}$ is the number of photons in mode $\displaystyle \omega_{n}$
- $\displaystyle \omega_{n}$ is the angular frequency for energy mode $\displaystyle n$
$\displaystyle Z=\frac{1}{1-e^{_{\hbar \omega \beta}}}$
- [Partition function] for photon gas