Hadron colliders offer a unique opportunity to test perturbative QCD b
ecause, rather than producing events at a specific beam energy, the dy
namics of the hard scattering is probed simultaneously at a wide range
of momentum transfers. This makes the determination of alpha(S) and t
he parton density functions (PDF's) at hadron colliders particularly i
nteresting. In this paper we restrict ourselves to extracting alpha(S)
for a given PDF at a scale which is directly related to the transvers
e energy produced in the collision. As an example, we focus on the sin
gle jet inclusive transverse energy distribution and use the published
1988-1989 CDF data with an integrated luminosity of 4.2 pb(-1). The e
volution of the coupling constant over a wide range of scales (from 30
to 500 GeV) is clearly shown and is in agreement with the QCD expecta
tion. The data to be obtained in the current Fermilab Tevatron run (ex
pected to be well in excess 100 pb(-1) for both the CDF and DO experim
ents) will significantly decrease the experimental errors.