# The Naked Scientists Forum

### Author Topic: How does temperature and pressure change in an expanding gas?  (Read 9739 times)

#### Supercryptid

• Hero Member
• Posts: 606
##### How does temperature and pressure change in an expanding gas?
« on: 11/04/2009 07:42:48 »
Let's say that I have a bottle of compressed gas. The volume of the compressed gas within the bottle is 1 cubic meter. The pressure is 10 atmospheres. The temperature is 300 Kelvins.

Now the bottle is opened and the gas is allowed to expand naturally into the air. I want to know what the temperature and volume of this expanding plume of gas will be once its pressure has fallen to 1 atmosphere. Assume that no heat energy is added to or taken away from this gas plume during this process. The ideal gas law doesn't seem to be helping me because I don't how much temperature and volume will change if the only factor known is how much the pressure has decreased.

This isn't for homework. It's for some personal calculations that I'm doing.

#### Vern

• Neilep Level Member
• Posts: 2072
##### How does temperature and pressure change in an expanding gas?
« Reply #1 on: 11/04/2009 14:44:10 »
I think it is the change in volume that causes the change in temperature. Volume is directly related to pressure, so equations relating pressure and temperature should work to predict changes in temperature.

#### lyner

• Guest
##### How does temperature and pressure change in an expanding gas?
« Reply #2 on: 12/04/2009 01:03:38 »
For an ideal gas, the P, V and T are related by the gas law

P1 V1 /T1  = P2 V2 /T2
T is the absolute temperature, in Kelvin, natch.

The temperature, being the average energy of the particles, must drop because the expansion has done work against the atmosphere and mechanical energy has been transferred to the surroundings.
Assuming this happens fast, the expansion will be 'adiabatic' but, after a while, the temperature will reach the ambient value and Boyle's law will apply.
This link, and many others, gives a good explanation.
http://www.av8n.com/physics/gas-laws.htm
He uses the term isentropic rather than adiabatic because it's more precise.
« Last Edit: 12/04/2009 01:16:05 by sophiecentaur »

#### The Naked Scientists Forum

##### How does temperature and pressure change in an expanding gas?
« Reply #2 on: 12/04/2009 01:03:38 »