= One-dimensional photon-gas thermodynamics
{title2=$U=\pi Lk_B^2T^2/(3\hbar c)$}
A cavity with two transverse <photon> <polarizations> and standing-wave spacing $\pi/L$ has <energy> <density of states> $2L/(\pi\hbar c)$. In the continuum regime, integrating the Bose occupation at zero <chemical potential> gives $U=bLT^2$, where $b=\pi k_B^2/(3\hbar c)$. The thermal quantities are $C_L=S=2bLT$, Helmholtz free <energy> $A=-bLT^2$ and generalized <pressure> $P=bT^2=U/L$. The last quantity has units of <force>. These thermal formulas exclude a separate boundary-dependent vacuum <energy> and require <temperature> above the mode-spacing scale.
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