# Rate of ideal gas expansion

1. Oct 11, 2004

### daniel3777

can anyone give me an equation for the rate that an ideal gas expands in a temperature change. like when a gas goes from 30 degrees to 50 degrees in a baloon. how quickly would it expand?

2. Oct 11, 2004

### mrjeffy321

you need to use the ideal gas law to figure it out.
Let P be the pressure of a gas, V the volume it occupies, and T its temperature (which must be in absolute temperature units, i.e., in Kelvin). Then the ideal gas law states

PV = nRT

where n is the number of moles of gas present and R is the universal gas constant, or equivalently

it would expand to the new volume as the gas temperature inccreases, there isnt a real amount of time it takes to expand, it just expands as the temperature increases. if the temperature were to suddenly increase by 20 degrees, then the gas would suddenly expand to the the new volume, but normaly it would be a gradual process because the temperture increasing is a gradual process.

3. Oct 12, 2004

### movies

Well, the ideal gas law is only valid for static systems, right? So I guess the answer would be that it would take as long as was needed for the system to re-equilibrate at the new parameters.

4. Oct 12, 2004

### chem_tr

Maybe you can try to use diffusion alternative... Diffusion rate changes in an indirectly proportional way with the molecular mass.

5. Oct 12, 2004

### gravenewworld

It seems to me that you would have to take the partial derivative of Volume with respect to T so you would get dV/DT=nR/P. So if pressure and amount of gas is held constant, the rate at which it expands is constant.

Last edited: Oct 12, 2004
6. Oct 12, 2004

### gravenewworld

This is basically the same thing that Guy-Lussac's law says. V=kT where k is some constant. So for example, if T doubles then volume will double (only if pressure and the amount of gas is held constant). Writing dV/dT=nR/P is just a more "sophisticated" way of stating the same thing.