[Thermodynamics] Transient Analysis of an air-filled tank

1. Oct 18, 2006

dav2008

Hey I think I'm missing something fundamental in this problem.

The problem reads: a 1 m3 tank initially contains air at 300 kPa, 300K. The air slowly escapes until the pressure drops to 100 kPa, via a process where pv1.2=constant (v being specific volume)

Find the heat transfer for a control volume enclosing the tank, assuming ideal gas behavior with constant specific heats.

I have determined the specific volumes of the initial and final states and I have looked up enthalpy and internal energy values for initial and final states. This is more of a symbolic question I have so I'll leave those out.

The energy balance (all for control volume, so I dont have to write cv over and over)

dU/dt = dQ/dt +(dm/dt)he where he is the enthalpy at the outlet valve.

Integrating with respect to time from state 1 to 2 would give m$$\Delta$$u=Q+(mf-mi)he

Now this is where I have several questions. 1) It seems like since the enthalpy is varying and not constant that I should have somehow considered that in the integration. I'm just not sure how I would approach the fact that the enthalpy at the outlet is varying over time.

I considered using the average of the initial and final enthalpies but that didn't yield a correct answer.

Thanks.