[Thermodynamics] Transient Analysis of an air-filled tank

[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 pv^1.2=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 don't have to write cv over and over)

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

Integrating with respect to time from state 1 to 2 would give m$$\Delta$$u=Q+(m_f-m_i)h_e

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.

 

[Almsco]

It's hard to answer this question without seeing the exact problem and what you have already tried. However, one thing to consider when dealing with a process where the enthalpy is changing over time is to use the energy equation in differential form. That way, you can account for any changes in enthalpy over time and get a more accurate result. You may also need to consider the mass flow rate and any heat transfer that occurs at the boundaries of the control volume.