Calculating volume of a gas under vacuum

[ports394]

If someone could help me out with this, I'd really appreciate it. It is work related, not homework.

I've got a vacuum dryer. There's a hot metal plate inside is heated with 240F steam. I'm assuming, after equilibrium that the plate is 240F. It'll be really really close.

The chamber is closed, and we pull 26.5 in. Hg vacuum on it. Basically ~3 psi absolute pressure.

The solution I'm evaporating is 50% ethyl alcohol, and 50% water. This mixture is by mass.

And I have 10 lb. of solution on the tray being heated/evaporated.


PV = nRT seems to work.
Now I've converted all my numbers to metric.

10.7 E3 (Pa) * V = ((10/2.2)Kg/32Kg E-3) * 8.314 * T
R= gas constant for my units..
T= what? Is it the boiling point of the solution at that vacuum temp, or is it the plate's 240F?

The goal here is to size a vacuum pump for the chamber, and I need a CFM/ACFM generated from the evaporation to pick the pump.

 

[PaoloPemi]

you can guess an average temperature for the mixture where it vaporizes, then calculate equilibria at that temperature and pressure, at that point you can define the heat added and the amount which vaporizes (or an equivalent procedure based on vacuum pump work for solving the problem), subtract that amount (at regular intervals via direct integration) and you'll get an idea of vapor compositions and flows.

 

[25362]

26.5 in Hg [≠] 3 psia.

At atmospheric pressure, a 50:50 w/w liquid mixture starts boiling at about 82^oC with a vapor that contains about 77% w/w ethanol, until the liquid reaches the azeotropic concentration at 78.2^oC, at which point the whole mixture would evaporate having 95.6% ethanol.

IMHO, the evacuation rate is linked to the heat input as PaoloPemi posted.

To design on the "safe side" without too much "overshoot", one can assume all vapors are water with the largest vapor specific volume of both.

 

[ports394]

http://www.engineeringtoolbox.com/vacuum-converter-d_460.html

That's the table I used to get ~26.5 in. Hg vacuum = 3.15 psia. I'll work on this a bit over the weekend and see where I get. I've just never seen calculations like this...not since high school anyway.

 

[chicopee]

760mmHg=29.92inHg=14.69psi
(29.92-26.5)*14.69/29.92=.066psia, that's the pressure at your vacuum reading of 26.5 inHg

 

[chemebabak]

http://www.engineeringtoolbox.com/vacuum-converter-d_460.html

That's the table I used to get ~26.5 in. Hg vacuum = 3.15 psia.

Per this table, 26.5 inHG vacuum (29.92 - 26.5 =3.42 inHG absolute) is close to 3.54 inHG absolute (88% vacuum). This corresponds to ~1.7 (not 3.15) psia.

760mmHg=29.92inHg=14.69psi
(29.92-26.5)*14.69/29.92=.066psia, that's the pressure at your vacuum reading of 26.5 inHg

Please review your calculations: 26.5 inHG vacuum = 3.42 inHG absolute = 1.68 psia.
(29.92-26.5)*14.69/29.92= 1.68 (not .066) psia= 11.6 kPa = 11,600 Pa

you can guess an average temperature for the mixture where it vaporizes, then calculate equilibria at that temperature and pressure, at that point you can define the heat added and the amount which vaporizes (or an equivalent procedure based on vacuum pump work for solving the problem), subtract that amount (at regular intervals via direct integration) and you'll get an idea of vapor compositions and flows.

What kind of process is this? Is this a batch process to vaporize and remove 10 lb out of 10 lb total? Is this a continuous process to vaporize and remove 10 lb/unit time? Really, [!]if you just want to size the pump then you need to know how fast you want to drawdown the 10 lb[/!] (or how much of the 10 lb/hr? that needs to be evaporated). First you must specify the time required, then you can calculate the vacuum pump flow rate required.

Also, you need to reconsider your procedure. At 1 atm, the 50%EtOH mixture boils at 185°F. Is the steam controlled so that the plate is constant at 240°F or greater? Are you maintaining the plate temp at 240°F to maintain a minimum vaporization rate? What is going on?

By the way, do not confuse CFM with ACFM with SCFM.
CFM is cubic feet per minute. This has no meaning.
ACFM is ACTUAL cubic feet per minute. This is measured at actual temperature and actual pressure.
SCFM is STANDARD cubic feet per minute. This is measured at Standard Temperature and Standard Pressure conditions: 60°F and 1 atm (14.7 psia).
Be careful, most compressors/ vac pumps are sized by SCFM and many vendors use CFM to mean SCFM.