  Well-known Mott's formula links the thermoelectric power characterised by
Seebeck coefficient to conductivity. We calculate analytically the
thermoelectric current and Seebeck coefficient in one-dimensional systems and
show that, while the prediction of Mott's formula is valid for Dirac fermions,
it is misleading for the carriers having a parabolic dispersion. We apply the
developed formalism to metallic single wall carbon nanotubes and obtain a
non-trivial non-monotonic dependence of the Seebeck coefficient on the chemical
potential. We emphasize that, in contrast to Mott's formula, the classical
Kelvin's formula that links thermoelectric power to the temperature derivative
of the chemical potential is perfectly valid in carbon nanotubes in the
ballistic regime. Interestingly, however, the Kelvin's formula fails in two-
and three-dimensional systems in the ballistic regime.
