  We study a series of relations between physical parameters in coronal loops
of the quiet Sun reconstructed by combining tomographic techniques and modeling
of the coronal magnetic field. We use differential emission measure tomography
(DEMT) to determine the three-dimensional distribution of the electron density
and temperature in the corona, and we model the magnetic field with a
potential-field source-surface (PFSS) extrapolation of a synoptic magnetogram.
By tracing the DEMT products along the extrapolated magnetic field lines, we
obtain loop-averaged electron density and temperature. Also, loop-integrated
energy-related quantities are computed for each closed magnetic field line. We
apply the procedure to Carrington rotation 2082, during the activity minimum
between Solar Cycles 23 and 24. We find a scaling law between the loop-average
density $N$ and loop length $L$, $N_m \sim L^{-0.35}$, but we do not find a
significant relation between loop-average temperature and loop length. We
confirm though the previously found result that loop-average temperatures at
the equatorial latitudes are lower than at higher latitudes. We associate this
behavior with the presence at the equatorial latitudes of loops with decreasing
temperatures along their length (``down'' loops), which are in general colder
than loops with increasing temperatures (``up'' loops). We find that the
obtained scalings for quiet-Sun loops do not generally agree with those found
in the case of AR loops from previous observational and theoretical studies. We
suggest that to better understand the relations found, it is necessary to
forward model the reconstructed loops using hydrodynamic codes working under
the physical conditions of the quiet-Sun corona.
