  In a flat 2-torus with a disk of diameter $r$ removed, let $\Phi_r(t)$ be the
distribution of free-path lengths (the probability that a segment of length
larger than $t$ with uniformly distributed origin and direction does not meet
the disk).
  We prove that $\Phi_r(t/r)$ behaves like $\frac{2}{\pi^2 t}$ for each $t>2$
and in the limit as $r\to 0^+$, in some appropriate sense.
  We then discuss the implications of this result in the context of kinetic
theory.
