A sealed, well-insulated 2000 thermos bottle with negligible heat capacity is co

Question

A sealed, well-insulated 2000 thermos bottle with negligible heat capacity is completely empty - a perfect vacuum. To this you add 550 of liquid nitrogen at its boiling point and a piece of scrap iron of mass "172 " initially at a temperature of 239K. Foolishly, the bottle is sealed tightly so that no gas can escape. You then hide the thermos under the professor's lectern, sneak out of the room, and await the inevitable explosion.
(This problem is alterred so that the MP "solution" is now correct. They had a mistake in the initial temperature of the iron, and they neglected the nitrogen vapor that should have been in the bottle at the start. The statement of the problem above now matches their answer.)

After a few seconds have passed, what is the pressure inside the thermos? The density of liquid nitrogen is 810

Explanation / Answer

I only have a minute, so I'll describe the steps...

find the volume of the iron, using density of 7.86 grams per mL

find the heat released by the iron when it is cooled from 239 K to 77 K (just use Q = mc deltaT)

find the mass of nitrogen turned to gas when it absorbs the heat (use Q = m L where L is latent heat of nitrogen)

find the number of moles of gas nitrogen using 1 mole per 28 grams (for N2 gas)

find the remaining mass of liquid nitrogen

find the volume of remaining liquid nitrogen, using density of 0.810 grams per mL

find the volume taken by the gas using

volume of thermos (i.e. 2000 mL) - volume of iron - volume of remaining liq nitr = ??

Finally... use ideal gas law. You know number of moles of gas, volume of gas, temperature of gas (77 K, the boiling pt of liq nitrogen). So you can calculate the pressure.

make sure you convert volume to liters first (1000 mL to one liter) and use

R = 0.08207 atm-L/mol K then your pressure will be in atmospheres.

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