  We present 7.5-14.2um low-resolution spectroscopy, obtained with the Spitzer
Infrared Spectrograph, of the T8.5 dwarf Wolf 940 B, which is a companion to an
M4 dwarf with a projected separation of 400 AU. We combine these data with
previously published near-infrared spectroscopy and mid-infrared photometry, to
produce the spectral energy distribution for the very low-temperature T dwarf.
We use atmospheric models to derive the bolometric correction and obtain a
luminosity of log L/Lsun = -6.01 +/- 0.05. Evolutionary models are used with
the luminosity to constrain the values of effective temperature (T_eff) and
surface gravity, and hence mass and age for the T dwarf. We further restrict
the allowed range of T_eff and gravity using age constraints implied by the M
dwarf primary, and refine the physical properties of the T dwarf by comparison
of the observed and modelled spectroscopy and photometry. This comparison
indicates that Wolf 940 B has a metallicity within 0.2 dex of solar, as more
extreme values give poor fits to the data - lower metallicity produces a poor
fit at lambda > 2um while higher metallicity produces a poor fit at lambda <
2um. This is consistent with the independently derived value of [m/H] = +0.24
+/- 0.09 for the primary star, using the Johnson & Apps (2008) M_K:V-K
relationship. We find that the T dwarf atmosphere is undergoing vigorous
mixing, with an eddy diffusion coefficient K_zz of 10^4 to 10^6 cm^2 s^-1. We
derive an effective temperature of 585 K to 625 K, and surface gravity log g =
4.83 to 5.22 (cm s^-2), for an age range of 3 Gyr to 10 Gyr, as implied by the
kinematic and H alpha properties of the M dwarf primary. The lower gravity
corresponds to the lower temperature and younger age for the system, and the
higher value to the higher temperature and older age. The mass of the T dwarf
is 24 M_Jupiter to 45 M_Jupiter for the younger to older age limit.
