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 beggining. 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.

 

[PJC01]

Hello,

Thank you for your question. The problem you have described is known as a thermo problem for a pressure vessel. This type of problem involves calculating the final pressure of a vessel after a certain amount of water has been heated to a specific temperature.

To solve this problem, we can use the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the temperature.

In this case, we can assume that the water vapor inside the vessel behaves as an ideal gas. We know that the initial pressure (P1) is atmospheric pressure, or 14.7 psi, and the initial temperature (T1) is 80°F. We also know that the final temperature (T2) is 1100°F and the final volume (V2) is 36.77ft^3.

To find the final pressure (P2), we can rearrange the ideal gas law equation to solve for P2:

P2 = (nRT2)/V2

To calculate n, the number of moles of water vapor, we can use the molar mass of water (18 g/mol) and the mass of water in the vessel (5 gal = 18.93 kg).

n = (18.93 kg)/(18 g/mol) = 1.05 mol

Substituting this value for n and the given values for R, T2, and V2 into the equation, we get:

P2 = (1.05 mol x 0.08206 L atm/mol K x 1100°F)/(36.77 ft^3)

P2 = 34.6 psi

Therefore, the final pressure of the vessel is 34.6 psi.

To create a curve relating the volume of water to the final pressure, you can repeat this calculation for different volumes of water (keeping the other variables constant) and plot the results on a graph. This will give you a relationship between volume and pressure for this specific system.

I hope this helps to clarify the problem and provide a solution. Please let me know if you have any further questions. Best of luck with your research!

Sincerely,

Scientist