  A differential emission measure (DEM) method is used to evaluate the
relationship of the electron density and temperature before and after a coronal
rain event during an active sun over the period from 20:10 UT on October 6 to
02:10 on October 7, 2011. Observational data were obtained from SDO/AIA for six
different extreme ultraviolet (EUV) spectral lines. 240 different coronal loops
were analyzed during this time interval, and the average electron density and
temperature were obtained using 171 {\AA} (Fe IX) and 193 {\AA} (Fe XII)
filters. The relationship between the density and temperature made it possible
to estimate the polytropic index in the solar corona before and after the
coronal rain. The polytropic index after the termination of the coronal rain
was estimated to be {\gamma} = 1.3{\pm}0.06, Which shows the usual
thermodynamic properties of study-state coronal plasma. The polytropic index at
the time of onset of the coronal rain was, however, estimated to be {\gamma} =
2.1{\pm}0.11, which indicates an unstable thermodynamic process, i.e., thermal
instability. It is suggested that the coronal rain is the result of an unstable
process, and the coronal plasma returns its stable state after the rain.
