  We consider a one-dimensional continuum gas of pointlike positive and
negative unit charges interacting via a logarithmic potential. The mapping onto
a two-dimensional boundary sine-Gordon field theory with zero bulk mass
provides the full thermodynamics (density-fugacity relationship, specific heat,
etc.) of the log-gas in the whole stability range of inverse temperatures
$\beta<1$. An exact formula for the excess chemical potential of a ``foreign''
particle of an arbitrary charge, put into the log-gas, is derived. The results
are checked by a small-$\beta$ expansion and at the collapse $\beta=1$ point.
The possibility to go beyond the collapse temperature is discussed.
