We use 3D radiation magnetohydrodynamic models to investigate how the thermodynamic quantities in the simulation are encoded in observable quantities , thus exploring the diagnostic potential of the C ii 133.5 { nm }  lines .
We find that the line core intensity is correlated with the temperature at the formation height but the correlation is rather weak , especially when the lines are strong .
The line core Doppler shift is a good measure of the line-of-sight velocity at the formation height .
The line width is both dependent on the width of the absorption profile ( thermal and non-thermal width ) and an opacity broadening factor of 1.2-4 due to the optically thick line formation with a larger broadening for double peak profiles .
The C ii 133.5 { nm }  lines can be formed both higher and lower than the core of the Mg ii k line depending on the amount of plasma in the 14–50 kK temperature range .
More plasma in this temperature range gives a higher C ii 133.5 { nm }  formation height relative to the Mg ii k line core .
The synthetic line profiles have been compared with IRIS observations .
The derived parameters from the simulated line profiles cover the parameter range seen in observations but on average the synthetic profiles are too narrow .
We interpret this discrepancy as a combination of a lack of plasma at chromospheric temperatures in the simulation box and too small non-thermal velocities .
The large differences in the distribution of properties between the synthetic profiles and the observed ones show that the C ii 133.5 { nm }  lines are powerful diagnostics of the upper chromosphere and lower transition region .