  We study the pressure, $P$, of SU($N$) gauge theory on a two-dimensional
torus as a function of area, $A=l/t$. We find a cross-over scale that separates
the system on a large circle from a system on a small circle at any finite
temperature. The cross-over scale approaches zero with increasing $N$ and the
cross-over becomes a first order transition as $N\to\infty$ and $l\to 0$ with
the limiting value of $2Pl/(N-1)t$ depending on the fixed value of $Nl$.
