Work needed to expand a very heavy gas under high pressure

[Gaspar_Paya]

Hi there, not sure if this is the right sub-forum. I hope so.

1. Homework Statement

This is the known data:

A isothermal process in the ascending conduit (like a chimney) of a closed-loop circuit, which is thermally insulated from the atmosphere, and in no contact with the air.

This is the data of the ascending conduit (chimney):
Initial Level L0: 0 meters
Final Level L1: 570 meters
Pressure at L0: 21 Bar // 2,100,000 Pa
Pressure at L1: 15 Bar // 1,500,000 Pa
Diameter at L0: 3.2 meters
Diameter at L1: 4.2 meters
Temperature at L0: 20 Celsius // 293.15 Kelvin
Temperature at L1: 20 Celsius // 293.15 Kelvin

The composition inside of the Chimney is a mixture of Sulfur Hexafluoride (SF6) and Nitrogen (N2). The Nitrogen remains gasified in the chimney, while 1,560 Kg of gasified SF6 at 20 Celsius enter into the chimney from the bottom L0, and exit gasified at 20 Celsius through the top L1.

Volume of SF6 at L0: 8.110 cubic meters
Volume of SF6 at L1: 13.663 cubic meters

I would like to know if is needed to supply heat to the ascending gasified SF6 while ascends and pushes up the column of gas that has over it, and if so, if the following equation and result are right:

Homework Equations

W istoherm = n R T Ln [ Vf / V1]

The Attempt at a Solution

Knowing that the Nitrogen does not expand inside of the chimney (it is fully expanded already) and that the molar mass of SF6 is 0.14606 Kg,

Is this solution right?

1,560 Kg of SF6 are 10680

W = 10,680.54 moles * 8.314462 [J / mol K] * Ln [13.663 / 8.110] = 46,319 Joules

I am not sure about this result, because the shown equation is from the Ideal Gas Law, that I understand is for noble gases at standard conditions of temperature and pressure... and my problem has a very high pressure and the gas has a very high density.

Thank you very much! :)

 

[Gaspar_Paya]

Hi Greg, thank you for your reply...

I tried to find an answer using another website, and the result is: 1.35778 x 10^7 J= 13.577 MJ

This is the page: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html

Which one is right? Any ideas or suggestions?

Thank you! :)

 

[Gaspar_Paya]

Hi everyone,

Thank you for the time you spent reviewing my questions.

After double checking my first post I realized that I did a HUGE and silly mistake. In my first equation I forgot to add the Temperature (T = 293.15 K). Once you add the temperature the result is almost exactly the same (13,578,428.208 J) than the one obtained from the Hyper Physics page.

Thank you! :)