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The expectation value of the complex phase factor of the fermion determinantis computed to leading order in the $p$-expansion of the chiral Lagrangian. Thecomputation is valid for $\mu<m_\pi/2$ and determines the dependence of thesign problem on the volume and on the geometric shape of the volume. In thethermodynamic limit with $ L_i \to \infty $ at fixed temperature $1/L_0$, theaverage phase factor vanishes. In the low temperature limit where $L_i/L_0$ isfixed as $L_i$ becomes large the average phase factor approaches one. Theresults for a finite volume compare well with lattice results obtained byAllton {\it et al}.. After taking appropriate limits, we reproduce previouslyderived results for the $\epsilon$-regime and for 1-dimensional QCD. Thedistribution of the phase itself is also computed.

The Approach to the Thermodynamic Limit in Lattice QCD at \mu\neq0