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We use linear viscous hydrodynamics to describe the energy and momentumdeposited by a fast moving parton in a quark gluon plasma. This energy-momentumis in turn used to compute the probability density for the production of softpartons by means of the Cooper-Frye formula. We use this probability density torender manifest a relation between the average transverse momentum given to thefast moving parton from the medium $\hat{q}$, the entropy density to shearviscosity ratio $\eta/s$ and the energy lost by the fast moving parton $\DeltaE$ in an expanding medium under similar conditions to those generated innucleus-nucleus collisions at the LHC. We find that $\hat{q}$ increaseslinearly with $\Delta E$ for both trigger and away side partons that have beenproduced throughout the medium. On the other hand, $\eta/s$ is more stable with$\Delta E$. We also study how these transport coefficients vary with thegeometrical location of the hard scattering that produces the fast movingpartons. The behavior of $\hat{q}$, with $\Delta E$ is understood as arisingfrom the length of medium the parton traverses from the point where it isproduced. However, since $\eta/s$ is proportional to the ratio of the length ofmedium traversed by the fast parton and the average number of scatterings itexperiences, it has a milder dependence on the energy it loses. This studyrepresents a tool to obtain a direct connection between transport coefficientsand the description of in-medium energy loss within a linear viscoushydrodynamical evolution of the bulk.

Relating $\hat{q}$, $\eta/s$ and $\Delta E$ in an expanding Quark-Gluon Plasma