  The 2.45 GHz plasma torch CO$_2\to$ CO + $\frac12$O$_2$ conversion experiment
[F A D"Isa et al. Plasma Sources Sci. Technol., vol. 29 (2020) 105009] has been
compared with thermo-chemical calculations. The 1.5D model of the
CO$_2$/CO/O$_2$/O/C mixture without turbulent transport has been used with
plasma acting only as prescribed heat source. The parameter range covered is
specific energy input SEI=0.3..5 eV/molecule at pressure $p$=0.9 bar, and
SEI=0.6..2 eV/molecule at $p$=0.5, 0.2 bar. The calculated conversion rates
$\chi$ are always in good agreement with experiment. At the same time, the
calculated temperatures $T$ may deviate significantly from the experiment,
especially for $p$=0.2 bar. The calculated $T$ were found to be sensitive with
respect to uncertain model parameters, but $\chi$ are not sensitive. The model
indicates that the conversion process is essentially two-dimensional and that
the main factor which reduces the energy efficiency is re-oxidation of CO
downstream from the plasma region. The proposed physico-chemical model
(chemical mechanism plus transport coefficients) can be suggested for practical
calculations for $p\geq$0.5 bar.
