  We use linear viscous hydrodynamics to describe the energy and momentum
deposited by a fast moving parton in a quark gluon plasma. This energy-momentum
is in turn used to compute the probability density for the production of soft
partons by means of the Cooper-Frye formula. We use this probability density to
render manifest a relation between the average transverse momentum given to the
fast moving parton from the medium $\hat{q}$, the entropy density to shear
viscosity ratio $\eta/s$ and the energy lost by the fast moving parton $\Delta
E$ in an expanding medium under similar conditions to those generated in
nucleus-nucleus collisions at the LHC. We find that $\hat{q}$ increases
linearly with $\Delta E$ for both trigger and away side partons that have been
produced throughout the medium. On the other hand, $\eta/s$ is more stable with
$\Delta E$. We also study how these transport coefficients vary with the
geometrical location of the hard scattering that produces the fast moving
partons. The behavior of $\hat{q}$, with $\Delta E$ is understood as arising
from the length of medium the parton traverses from the point where it is
produced. However, since $\eta/s$ is proportional to the ratio of the length of
medium traversed by the fast parton and the average number of scatterings it
experiences, it has a milder dependence on the energy it loses. This study
represents a tool to obtain a direct connection between transport coefficients
and the description of in-medium energy loss within a linear viscous
hydrodynamical evolution of the bulk.
