What pressure does liquid nitrous oxide need at -45°C to remain liquid? How can I calculate it's pressure required for other temperatures?


This document provides a formula for the vapour pressure of $N_2O$:

$$ log_e \left(\frac{p}{p_c}\right) = \frac{1}{T_r}\left[b_1(1-T_r) + b_2(1-T_r)^{3/2} + b_3(1-T_r)^{5/2} + b_4(1-T_r)^5\right]$$

where $p$ is the pressure you want to solve for, $p_c = 7251$kPa, $b_1 = -6.71893$, $b_2 = 1.35966$, $b_3 = -1.3779$, $b_4 = -4.051$, $T_r = T / 309.57$K, and $T$ is the temperature.

This is valid over the range $T = -90$ to $36^o$C ($183.15$ to $308.15$K).

There might well be simpler ways to get an approximate answer from molecular theory / thermodynamics, but if you just practically want to calculate it this looks like it would be okay.


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