We present high-resolution (~2.5) observations of 12CO J=6-5 towards the luminous infrared galaxy VV 114 using the Submillimeter Array. We detect 12CO J=6-5 emission from the eastern nucleus of VV 114 but do not detect the western nucleus or the central region. We combine the new 12CO J=6-5 observations with previously published or archival low-J CO observations, that include 13CO J=1-0 Atacama Large Millimeter/submillimeter Array cycle 0 observations, to analyze the beam-averaged physical conditions of the molecular gas in the eastern nucleus. We use the radiative transfer code RADEX and a Bayesian likelihood code to constrain the temperature (T_kin), density (n(H2)) and column density (N(12CO)) of the molecular gas. We find that the most probable scenario for the eastern nucleus is a cold (T_kin = 38 K), moderately dense (n(H2) = 10^2.89 cm^-3) molecular gas component. We find the most probable 12CO to 13CO abundance ratio ([12CO]/[13CO]) is 229, roughly three times higher than the Milky Way value. This high abundance ratio may explain the observed high 12CO/ 13CO line ratio (> 25). The unusual 13CO J=2-1/J=1-0 line ratio of 0.6 is produced by a combination of moderate 13CO optical depths (tau = 0.4 - 1.1) and extremely subthermal excitation temperatures. We measure the CO-to-H2 conversion factor, alpha_co to be 0.5 M_sol (K km s^-1 pc^2)^-1, which agrees with the widely used factor for ultra luminous infrared galaxies of Downes & Solomon (1998; alpha_co =0.8 M_sol (K km s^-1 pc^2)^-1).
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