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ideal gas law help- N2 gas and H2O sparging under vacuum- oil deodorizing


I am heating the liquid contents of my chemical reactor to 90C by heating the external jacket. It is a closed system under vacuum at about -27inHg w/ a vacuum pump constantly evacuating the system. I am heating H2O to 90C in an open system. I open the inlet valve and allow a small volume of water to enter the vacuum reactor. Once it enters the vacuum, the boiling point of the H20 drops, the H2O evaporates, and it cools the contents of our reactor.

I would like to avoid the cooling effect from the evaporation by switching to hot N2. My N2 tank has a headspace pressure of 2000PSI. I will use a regulator to regulate it down to somewhere below 40 PSI. I will place an inline gas heater between my regulator and my on/off intake valve on the chemical reactor. My question is this- at what temperature does my N2 gas have to be at 40PSI so that it enters the -27inHg vacuum at 90C, avoiding the overheating or overcooling of the contents of my reactor?

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