An approximate theory, including effects of the density, for the equil
ibrium properties of a polymer lattice model (bond-fluctuation model)
is presented and compared with Monte Carlo simulations. Effects of the
density are taken into account by balancing the volume requirements o
f the individual bond vectors with the pressure that a melt exerts at
a given density. This simple theory yields rather accurate (to within
a few percent) estimates for the chain length and temperature dependen
ce of various quantities that scan different length scales of the poly
mers (bond length, radius of gyration, etc.). With the inclusion of th
e density, one can also design an improved definition of an internal t
emperature of the melt, which is distinct from the external temperatur
e of the surrounding heat bath. When the melt falls out of equilibrium
during the vitrification process, this internal temperature is expect
ed to measure the temperature that the melt actually experiences, and
may thus serve to eliminate the nonequilibrium effects from the simula
tion data. The extent to which this expectation is borne out by a comp
arison with the simulation is addressed.