Looks good. "Cooling" is what happens to the other materials when dry ice sublimes. The surroundings provides the sublimation heat to dry ice. -57°C is just nonsense to me: depending on he conditions, you nearly reach the sublimation temperature.
-57°C is not a pure nonsense - it is the freezing point of carbon dioxide.
So, if you have liquid carbon dioxide and release pressure on it, it cools. At pressure of slightly over 5000 mbar, it reaches temperature -57 degrees, at which point it freezes.
The solid continues to sublime. At pressure of 1000 mbar, it reaches temperature -78 degrees.
But note that the partial pressure of carbon dioxide is not 1000 mbar! It is 0,4 mbar - used to be 0,3.
The vapour pressure of carbon dioxide reaches 0,4 mbar at around -140 degrees.
Does dry ice remain at -78 degrees where its vapour pressure 1000 mbar is far in excess of its partial pressure, or does it continue cooling until it reaches its partial pressure, at -140 degrees?