  We consider the motion of a system of free particles moving on a plane with
regular hard polygonal scatterers arranged in a random manner. Calling this the
Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a
finite-time exponent to characterize its dynamics. As the number of sides of
the polygon goes to infinity, when polygon tends to a circle, we recover the
usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To
obtain this result, we generalize the reflection law of a beam of rays incident
on a polygonal scatterer in a way that the formula for the circular scatterer
is recovered in the limit of infinite number of vertices. Thus, chaos emerges
from pseudochaos in an appropriate limit.
