Thermodynamics of matter under pressure

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EEstudentNAU
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Imagine a tank with dry ice under high pressure, 150 psi or higher. A pipe carrying a fluid (with a freezing point lower than the temperature of the tank) passes through the tank with an initial temperature much higher than the tank.

What will happen to the dry ice? I assume the temperature of the tank will rise because of the hotter fluid passing through. Will the pressure rise as well?
 
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If you raise the temperature of a closed vessel the pressure will go up, no matter what's in it.
 
Please look here: pressure-temperature phase diagram of CO2:
http://en.wikipedia.org/wiki/File:Carbon_dioxide_pressure-temperature_phase_diagram.svg"
If conditions are in blue region then dry ice will melt.
In red region will remain solid.
 
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