Pressure of sealed in liquid nitrogen

If you

1. take a container of great strength,
2. fill it to the brim with liquid nitrogen,
3. seal the container, and
4. heat it to room temperature.

What will the pressure be inside?

Bonus: The same with liquid Helium.

(I posted this Reference for phase diagrams of elements , but the answer here can not be read from the phase diagram.)

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 My guess is that the only way to answer this question, even remotely correct, is to do an experiment. – Pygmalion Jun 4 '12 at 21:03 @Pygmalion: A very dangerous experiment, if you do not have a rough estimate :o) – Hans-Peter E. Kristiansen Jun 4 '12 at 21:05 Hear hear!...... – Pygmalion Jun 4 '12 at 21:11

For an ideal gas in a closed 1L container this would result in a pressure of 700 atm according to $$P V = n R T$$ From the phase diagram nitrogen is a gas at standard pressure and becomes supercritical at approximately 100 atm. The ideal gas law can therefore only be a guideline well below this pressure. To incorporate the intramolecular forces the van der Waals equation is the next best choice: $$\left(p + \frac{n^2 a}{V^2}\right)\left(V-nb\right) = nRT$$ With the coefficient $b$ for nitrogen ($3.85 \cdot 10^{-5}$ m$^3$/mole from here) the minimum volume for 1L of liquid nitrogen (31 mole) is 1.2L. So even the correction to the ideal gas law cannot capture the full range.