Temperature change after flow through an oriface

[gbq57]

I'm interested in modelling the effect of a chamber of ideal gas at a high pressure passing through subsequent chambers of lower pressure gas - each subsequent chamber joined to the previous via a thin plate oriface.

I'm looking at at an iterative solution (i don't do integrals) and i am happy that i can calculate the instantaneous flow of gas through an orifice between chambers - whether chocked or not.

I can not find how to calculate the temperature change of the gas in each of the chambers either side of the orifice as a result of the flow (assuming no 'velocity' of gas remains in any of the chambers).

There is no work being done in the system and I know during a free adiabatic expansion the temperature is constant but this scenario is different - I assume temperature/internal energy will drop in the high pressure side and increase in the low pressure side as the gas passes through the orifice - but by how much - can someone point me to a formula or another way of looking at the problem?

 

[gbq57]

Ok - let's put some real figures on this to get the ball rolling...

Assume the gas concerned is air - 29 mol/g, k=1.4

Chamber A has 5g of air (0.1724 mols) in 1 litre at 1000 Kelvin.
P=nRT/V
pressure = 1.433Mpa
density = 5g/l (5kg/m3)

Chamber B has 2.4g of air (0.0827 mols) in 2 litres at 300 Kelvin
pressure = 0.103Mpa
density = 1.2 g/l

The chambers are connected by a 10mm diameter orifice with a discharge Coefficient (C) of 0.76

If the orifice was opened for approx 4.7 milliseconds then closed then I calculate around 0.5 grams of gas would rush under choked conditions to chamber B. But what would the pressure/temperature be in both of the chambers assuming no loss of energy outside the system?

any help, informed guesses, discussion is welcome!

 

[gbq57]

any one - am I asking something difficult/unknown?