  We consider a one-dimensional gas of positive and negative unit charges
interacting via a logarithmic potential, which is in thermal equilibrium at the
(dimensionless) inverse temperature $\beta$. In a previous paper [Samaj, L.: J.
Stat. Phys. 105, 173-191 (2001)], the exact thermodynamics of the unrestricted
log-gas of pointlike charges was obtained using an equivalence with a
(1+1)-dimensional boundary sine-Gordon model. The present aim is to extend the
exact study of the thermodynamics to the log-gas on a line with alternating
$\pm$ charges. The formula for the ordered grand partition function is obtained
by using the exact results of the Thermodynamic Bethe ansatz. The complete
thermodynamics of the ordered log-gas with pointlike charges is checked by a
small-$\beta$ expansion and at the collapse point $\beta_c=1$. The inclusion of
a small hard core around particles permits us to go beyond the collapse point.
The differences between the unconstrained and ordered versions of the log-gas
are pointed out.
