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[FJK]

Hi All,

This is a question from a Thermodynamic Basic Quiz that seems interesting to me. I would like to see some other suggestion on how to solve this problem. Here it go:

In some industry they have two plants that uses gas for their burners. The gas is stored in one horizontal cilindrical vessel (length and diameter known, perfectly insulated) with a thin, frictionless, adiabatic piston that separates the gas that uses Plant A from the gas of Plant B. The two plants consume this gas (consider that the gas is a pure gas) at different rates and in some point the vessel need to be refilled. When they refill the vessel they put the piston at the middle of the cilinder and make the temperature in both sides equal.

Now, considering that you can use only manometers and thermometers as instruments and that at any point you can see the piston's position in the vessel, what is the minimum number of these instruments that you need to know the consumption of gas of each plant and how you calculate it.

The same problem comes again but now cosidering that the gas is not pure but a mixture with known composition.

I may admit that I'm a little bit rusty on my thermodynamic knowledge and that I prefer this kind of problem when there is no limitation on the instruments (in wich case I may use two flowmeters and save all the calculations needed) but on its original form I solve this problem considering the gas as non-ideal and using one manometer on the vessel and one termometer on each side of the vessel. To calculate the gas consumption I only need to use this values to calculate the specific volume of the gas (with the proper EoS) on each side and then, with the piston's position, determine the actual volume of each side. At this point I only divide the two values and obtain the number of moles of gas at the end. This way I can know the consumption of gas of each plant.

If anyone know other way with less instruments then please let me know it.

Thank You

FJK

[abhi_agrawa]

Assumption 1. The gas is known
Assumption 2. The consumption os gas is slow enough, to allow for thermal equilibrium in the two partitions.

The we need 1 pressure guage/manometer and 1 thermometer.

Procedure:
At the initial condition the pressure and the temperature is measured. The volume of each partition is also known (as the geometric parameters of the vessel are known). Hence, by using a suitable EOS, the initial number of moles is known.

After some time, the temperature and pressure are measured again. The number of moles of gas in each partition can again be determined. Now the rate of consumption can be found out.

If under the storage conditions, the gas does not liquify, then the above thing is valid for gas mixtures also. Else the phase equilibrium will have to be taken in account.