We perform detailed spectroscopic analysis and numerical modelling of an H2-bearing damped Lyman-alpha absorber (DLA) at zabs = 2.05 towards the quasar FBQS J2340-0053. Metal absorption features arise from fourteen components spread over $Delta v_{90}$ = 114 km s$^{-1}$, seven of which harbour H2. Column densities of atomic and molecular species are derived through Voigt profile analysis of their absorption lines. We measure total N(H I), N(H2) and N(HD) to be 20.35+/-0.05, 17.99+/-0.05 and 14.28+/-0.08 (log cm$^{-2}$) respectively. H2 is detected in the lowest six rotational levels of the ground vibrational state. The DLA has metallicity, Z = 0.3 Z$_sun$ ([S/H] = -0.52+/-0.06) and dust-to-gas ratio, $kappa$ = 0.34+/-0.07. Numerical models of the H2 components are constrained individually to understand the physical structure of the DLA. We conclude that the DLA is subjected to the metagalactic background radiation and cosmic ray ionization rate of $sim$ 10$^{-15.37}$ s$^{-1}$. Dust grains in this DLA are smaller than grains in the Galactic interstellar medium. The inner molecular regions of the H2 components have density, temperature and gas pressure in the range 30-120 cm$^{-3}$, 140-360 K and 7,000-23,000 cm$^{-3}$ K respectively. Micro-turbulent pressure is a significant constituent of the total pressure, and can play an important role in these innermost regions. Our H2 component models enable us to constrain component-wise N(H I), and elemental abundances of sulphur, silicon, iron and carbon. We deduce the line-of-sight thickness of the H2-bearing parts of the DLA to be 7.2 pc.
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