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PVT type Calculation
Slater - 22/6/12 at 09:57 AM

Here's a question for Locosters Friday!!!

If I have a fixed volume gas tank with a volume of 1.65 cubic m, at the start the pressure is zero (or atmospheric),
after 24 hrs the pressure is 150 psi
after 48 hrs the pressute is 290 psi
after 72 hrs the pressure is 420 psi

What volume of gas is being pumped in the tank per day to give the 140 psi per day increase?

I know it's probably a PVT type Boyles law calculation but I cant get my head round it.
Help....
Keith.

britishtrident - 22/6/12 at 10:33 AM

Volume varies with temperature

Working in absolute metric SI units for pressure and temperature.

With a gas at a steady temperature Pressure x Volume = constant

What you really need to find is the mass of gas being pumped in

for a Gas PV= MRT

Re-arange to find Mass (PV)/(RT) = M

Where R is the specific gas constant for the gas.

You can then find the increase in mass each day and by re-arranging the formula find the volume pumped at standard temperature and pressure.

MRT/P =V

SeanStone - 22/6/12 at 10:39 AM

I don't know as you're able to get an answer to that question?

Surely the volume is dictated by what it is contained by?

In this instance the volume stays the same, so the pressure and temperature change

The air will be coming from the atmosphere, in which case, your 'volume of gas' would probably be a decimal of the amount of air taken from the atmosphere and put into the container...

Volumes aren't pumped. you don't take 1cm^3, put it in a 2cm^3 space and have it only take up 1^3. The gas will expand and take up the whole volume, but the pressure and temperature will be lower

Think I'm around about there, but hopefully someone else will confirm/correct me!

Slater - 22/6/12 at 10:50 AM

We will assume the temp is constant for simplicity.

R for natural gas is 518 in SI units.

SeanStone - 22/6/12 at 11:26 AM

is it a balloon?

Slater - 22/6/12 at 11:51 AM

Sorted............. thanks guys

1.494479618 cu m 0-24 hrs
0.79867832 cu m 24-48 hrs
0.512077631 cu m 48-72 hrs

This site is the best.

cliftyhanger - 22/6/12 at 01:12 PM

quote:
Originally posted by britishtrident
Volume varies with temperature

Working in absolute metric SI units for pressure and temperature.

With a gas at a steady temperature Pressure x Volume = constant

What you really need to find is the mass of gas being pumped in

for a Gas PV= MRT

Re-arange to find Mass (PV)/(RT) = M

Where R is the specific gas constant for the gas.

You can then find the increase in mass each day and by re-arranging the formula find the volume pumped at standard temperature and pressure.

MRT/P =V


I always had it as PV=nRT
n being the number of moles....

(just checked, in BT's case it is also correct, but he should have used a small r as it is gas constant per unit mass!)

SeanStone - 22/6/12 at 01:13 PM

How has the volume changed in something that has a fixed volume?

Peteff - 23/6/12 at 08:00 AM

quote:
Originally posted by SeanStone
How has the volume changed in something that has a fixed volume?


Could it be because of the pressure variation ?

coyoteboy - 23/6/12 at 09:16 AM

That would be a density change, not a volume change.

britishtrident - 23/6/12 at 02:10 PM

I take the OP to mean the equivalent volume at STP

geoff shep - 23/6/12 at 08:03 PM

PV=constant

so,

if the pressure's gone up 10 times, (atmospheric pressure is approx 15psi) then there's 10 times the original amount of gas in there.

So you've got 16.5 cubic m worth of gas in there after one day - well actually it's only taking up 1.65 cu m of space cos that's the volume of the cylinder, but if you let it out (and kept it's temperature constant) it would take up 16.5 cu m.

You need to be specific about the starting pressure. If it was zero, i.e. a vacuum, then you've pumped in 16.5 cu m. If it was atmospheric, you've pumped in an additional 14.85 cu m.

(290 to 420 is only a rise of 130 psi BTW)