  We derive distributions of dust temperature and dust opacity across M31 at
45" resolution using the Spitzer data. With the opacity map and a standard dust
model we de-redden the Ha emission yielding the first de-reddened Ha map of
M31. We compare the emissions from dust, Ha, HI and H2 by means of radial
distributions, pixel-to-pixel correlations and wavelet cross-correlations. The
dust temperature steeply decreases from 30K near the center to 15K at large
radii. The mean dust optical depth at the Ha wavelength along the line of sight
is about 0.7. The radial decrease of the dust-to-gas ratio is similar to that
of the oxygen abundance. On scales<2kpc, cold dust emission is best correlated
with that of neutral gas and warm dust emission with that of ionized gas. Ha
emission is slightly better correlated with emission at 70um than at 24um. In
the area 6kpc<R< 17kpc, the total SFR is ~0.3Msun/yr. The Kennicutt-Schmidt law
between SFR and total gas has a power-law index of 1.30+-0.05 in the radial
range of R=7-11kpc increasing by about 0.3 for R=11-13kpc. The lack of H2 in
the central region could be related to the lack of HI and the low opacity/high
temperature of the dust. Since neither SFR nor SFE is well correlated with the
surface density of H2 or total gas, other factors than gas density must play an
important role in the formation of massive stars in M31. The molecular
depletion time scale of 1.1 Gyr indicates that M31 is about three times less
efficient in forming young massive stars than M33.
