Thermo problem for a pressure vessel

[rkendrick]

Homework Statement

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

Homework Equations

Steam Tables

The Attempt at a Solution

i've used many approaches such as heat transfer finding the Q, and the ideal gas law.

 

[RTW69]

Constant volume: P₁/T₁=P₂/T₂

 

[rkendrick]

can this combined law be applied to superheated steam? i didn't think it could since i came up with 76 psia which couldn't be correct

 

[RTW69]

You are correct, my mistake. You know the specific Volume (volume/mass) and the final temperature. Look on your superheated Water Vapor charts to find the pressure.

 

[rkendrick]

Finding the specific volume, I get that 36.77cu.ft./ (5*8.33lb/gal) = 0.8828 which corresponds to a pressure of 1000psia from the superheated steam tables at 1100°F. It seems to me that the pressure should be more around the 7000-10,000 psia range, is this correct?

 

[RTW69]

I think 1000 psia is correct.

 

[LawrenceC]

The steam table is the correct route to take. As previously stated, you know the specific volume and you know the temperature. Therefore you can find the pressure from the steam tables as noted above.

 

[rkendrick]

sounds good, thanks guys!