Thermo problem for a pressure vessel

[rkendrick]

My question has to do with heating water to a superheated state inside a constant volume vessel.

Given: A pressure vessel with a total volume of 36.77ft^3, is filled with 5 gal of water and heated from room temp. to a final temp. of 1100°F. Obvisouly the initial pressure is atmospheric and the initial temp. is room, or let's say 80°F.

Find: Final pressure of vessel.

In the end I will vary the amount of water in the vessel to obtain a curve relating the volume of water to the final pressure but we can assume 5 gal for the beginning. I have worked on this for some time and am sure that it is much simpler than I am making it out to be. I am aware that the Ideal Gas Law may not be applied since the gas will be water vapor at a high pressure. Hopefully one of you can enlighten me.

Thanks

 

[Philip Wood]

I note that the container is not, in fact, filled with water, as 5 US gallons occupy only 0.664 ft².

Your first step is to look up the saturated vapour pressure, p_sat, of water at 1100°F. You should now use the ideal gas equation to calculate the number of moles of steam there would be in the container, at a (partial) pressure of p_sat. Make sure it's less than the number of moles in 5 gallons of water.

If it is less, than the water, won't have run out, and to find the pressure in the container you simply add P_sat (the partial pressure of the steam) to the partial pressure, p_air, of the air at 1100 °F, which will be approximately
p_{air} = \frac{1100 + 460}{80 + 460} \times p_{atmos}.

If the number of moles of steam in the container at 1100 °F and p_sat is greater than the number of moles in 5 gallons of water then the water will run out (all evaporated) at some temperature lower than 1100 °F and you will need to modify your calculation. If you can't figure out how to do this, ask again!

Good luck!

 

[rkendrick]

My saturated steam tables only go up to 705.1°F which I assume is the critical temperature. How would I find the Psat for 1100°F? Also, if I am well above the critical temperature is it not safe to assume that all the water is now evaporated?

 

[Philip Wood]

rkendrick. You are quite right. I'd simply find how many moles of water vapour there are in 5 gallons of water, and treat the water vapour as an ideal gas, in order to calculate the partial pressure at 1100 °F. Of course the ideal gas bit is an approximation, but to do anything else would be rather complicated. Incidentally, 1100 °F is too low a temperature for appreciable thermal dissociation of water molecules.