Expansion of gas into a vacuum

[capanni]

I have two scenarios.

Scenario one:
Consider an ideal gas in a flask F_1 of Volumne V_i = 1 m^3 at P_i = 8.0 atm
this is connected by a valve to a second flask F_2 so that the combination of F_1 & F_2 gives a volume V_f = 4 m^3.

When the valve is opened (instantly) the gas flows from F_1 to F_2 until the pressure is equalised.

Initial_________________Final
V_i = 1 m^3 V_f = 4 ^m3
P_i = 8.0 atm P_f = 2.0 atm
T_i = 298K T_f = 298K

With an ideal gas, no work is done.

Question, how long does it take for the gas to flow from F_1 to F_2, assuming the valve and connecting tube have no length. The flasks, if spheres would have approximate radius 0.62m and 0.895m respectively. The aperture between them is 0.1 m^2.

Scenario two:
This one may actually be easier.
Consider a perfect gas as before. In this case spherical flask F_1 is suspended centrally (by magic) inside flask F_2. All other things are the same as before.

Initial_________________Final
V_i = 1 m^3 V_f = 4 ^m3
P_i = 8.0 atm P_f = 2.0 atm
T_i = 298K T_f = 298K

Except because F_1 is inside F_2, the radius of F_2 is now approximately 0.985 m.
So that vol F_1 = V_i = 1 m^3 and vol F_2 = V_f = 4 m^3.

Question, if the shell of f_1 was to instantly be removed, how long does it take for the gas to expand into F_2?

 

[Valerie Park]

Assuming there is no work done, the time taken for both scenarios would be the same. To calculate this, we need to use the ideal gas law. The ideal gas law states that PV=nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant and T is temperature. For scenario one, the time taken can be calculated as follows: Time = (V_f - V_i)/(A*sqrt((P_i*V_i)/(n*R*T_i))) Where A is the aperture between the flasks.For scenario two, the time taken can be calculated as follows:Time = (V_f - V_i)/(A*sqrt((P_i*V_i)/(V_f*n*R*T_i))) Where A is the aperture between the flasks.Therefore, the time taken for both scenarios would be the same.