# Speed of gas expansion & Size of expansion

1. Jul 25, 2007

### s.p.q.r

Hi,

Ive a couple of questions.

1) Ideal gases expand according to temperature. But how quickly does it take for it to expand to its destined size?

Lets say if I had 100 moles of Argon and heated it to 373kelvins. How long would it take for it to expand to it final size?

2) To what size will 100 moles of Argon heated to 373kelvins expand? How many litres?

Cheers gang.

2. Jul 25, 2007

### mgb_phys

It depends on how quickly you heat it!
And on the speed of sound in the gas, if you start heating one side of the sample the other side will only feel the heat when it has travelled through the sample - which it does at the speed of sound. To make it a little more complicated, the speed of sound in a gas depends on the temperature!

1 mole of an ideal gas is 22.4 litres at 273K (0deg C).
You don't say what temperature you started with 100l at but assuming it was 0degC the final volume = (373/273) * 22.4l/mole = 30.6 l/mole

3. Jul 25, 2007

### s.p.q.r

Great, lets say that the entire container was 100deg C automatically. How long would it take to reach its final expansion size?

And for the answer to the second question, i dont understand, could you clarify? Thanks.

4. Jul 25, 2007

### mgb_phys

In real life it is difficult to work out, it depends on the shape of the container the initial temperature of the gas and turbulent motions of the gas.
If you heated the entire container instantly and uniformly you might not get the quickest heating of the gas as there would be no convection.
I'm not being deliberately difficult, designing heat exchangers has been a big field of study for nearly 200years, since the first steam engines.

Ideal gases always occupies 22.4L/mole at 273kelvin/1 atmosphere ( called standard temperature and pressure - STP)
As you heat the gas the expansion in volume is proportional to temperature, so if you double the temperatue you double the volume.

You don't say what temperature you started with 100moles at! If it is currently at 0deg C and you heat it to 100degC it will obviously expand more than if you are currently at 90degC and only heating it another 10deg.

5. Jul 26, 2007

### s.p.q.r

Sorry. Its heated to 25 degrees C.

6. Jul 26, 2007

### mgb_phys

You mean heated from 25deg right?

As I said 1 mole at 273K = 22.4L
So 1 mole at 25deg C is ((273+25)/273) * 22.4
and 1 mole at 100deg C is ((273+100)/273) * 22.4
The expansion is the difference.