We investigate the physical properties of the interstellar medium (ISM) in the merging pair of galaxies known as The Antennae (NGC 4038/39), using the deep coadded ~411 ks Chandra ACIS-S data set. The method of analysis and some of the main results from the spectral analysis, such as metal abundances and their variations from ~0.2 to ~20-30 times solar, are described in Paper I (Baldi et al. submitted). In the present paper we investigate in detail the physics of the hot emitting gas, deriving measures for the hot-gas mass (~10^ M_sun), cooling times (10^7-10^8 yr), and pressure (3.5x10^-11-2.8x10^-10 dyne cm^-2). At least in one of the two nuclei (NGC 4038) the hot-gas pressure is significantly higher than the CO pressure, implying that shock waves may be driven into the CO clouds. Comparison of the metal abundances with the average stellar yields predicted by theoretical models of SN explosions points to SNe of Type II as the main contributors of metals to the hot ISM. There is no evidence of any correlation between radio-optical star-formation indicators and the measured metal abundances. Although due to uncertainties in the average gas density we cannot exclude that mixing may have played an important role, the short time required to produce the observed metal masses (<=2 Myr) suggests that the correlations are unlikely to have been destroyed by efficient mixing. More likely, a significant fraction of SN II ejecta may be in a cool phase, in grains, or escaping in hot winds. In each case, any such fraction of the ejecta would remain undetectable with soft X-ray observations.
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