  To understand how the evolution of grain size distribution in galaxies
affects observed dust properties, we apply a post-processing dust evolution
model to galaxy merger trees from the IllustrisTNG cosmological hydrodynamical
simulation. Our dust model includes stellar dust production, sputtering in hot
gas, dust growth by accretion and coagulation in the dense interstellar medium
(ISM), and shattering in the diffuse ISM. We decompose the grain size
distribution into different dust species depending on the elemental abundances
and the dense ISM fraction given by the simulation. In our previous work, we
focused on Milky Way (MW) analogs and reproduced the observed MW extinction
curve. In this study, we compute dust spectral energy distributions (SEDs) for
the MW analogues. Our simulated SEDs broadly reproduce the observed MW SED
within their dispersion and so does the observational data of nearby galaxies,
although they tend to underpredict the MW SED at short wavelengths where
emission is dominated by polycyclic aromatic hydrocarbons (PAHs). We find that
metallicity and dense gas fraction are the most critical factors for the SED
shape, through their influence on coagulation and shattering.The overall
success of our models in reproducing the MW SED further justifies the dust
evolution processes included in the model and predicts the dispersion in the
SEDs caused by the variety in the assembly history. We also show that the most
significant increase in the dust SED occurs between redshifts $z\sim 3$ and 2
in the progenitors of the simulated MW-like galaxies.
