  Assuming that 1-dimensional self-assembly nanotubes can be represented as a
1-dimensional cavity-type black-body radiator of length L and radius r in
thermal equilibrium at a temperature T, analytical expressions for the thermal
radiative and thermodynamic functions of the emitted black-body radiation are
obtained in the finite spectral range of the electromagnetic spectrum. The
total energy density, the Stefan-Boltzmann law, the number density of the
photons, the Helmholtz free energy density, the entropy density, the heat
capacity at constant volume, and the pressure are expressed in terms of the
polylogarithm functions. In the frequency range 0.05-0.19 PHz, the thermal
radiative and thermodynamic functions of the 1-dimensional black-body radiation
at different temperatures are calculated. To confirm our assumption, it is
necessary to measure the total energy density in the direction L in the finite
frequency range 0.05-0.19 PHz, using a single nanoparticle mass spectrometer or
other optical devices.
