[Thermodynamics] Transient Analysis of an air-filled tank

In summary, the conversation revolves around finding the heat transfer for a control volume enclosing a tank with changing pressure and volume. The suggested approach is to use the energy equation in differential form to account for any changes in enthalpy over time, as well as considering the mass flow rate and any heat transfer at the control volume boundaries.
  • #1
dav2008
Gold Member
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1
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 don't 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[tex]\Delta[/tex]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.
 
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  • #2
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.
 
  • #3


I would respond by saying that your approach of using the energy balance equation is a good start. However, in order to properly account for the varying enthalpy at the outlet, you would need to consider the work done by the escaping air. This would involve integrating the pressure-volume relationship given in the problem (pv^1.2=constant) over time to determine the work done. This work would then need to be included in the energy balance equation, along with the heat transfer and change in internal energy terms.

Additionally, you may need to take into account the change in specific heats of the air as it expands and cools. This would require using the average specific heat values over the temperature range in the problem.

I would also suggest checking your calculations and units to ensure that everything is consistent and that the final answer makes sense in the context of the problem. It may also be helpful to consult a textbook or reference material on transient analysis in thermodynamics to guide your approach.
 

1. What is transient analysis in the context of an air-filled tank?

Transient analysis in thermodynamics refers to the study of a system's behavior as it moves from one state to another. In the case of an air-filled tank, this involves examining how the temperature, pressure, and volume of the air inside the tank change over time.

2. Why is transient analysis important in studying air-filled tanks?

Transient analysis allows us to understand how the air inside the tank responds to changes in external conditions, such as temperature or volume. This is crucial in designing and optimizing air-filled tanks for various applications, such as in HVAC systems or compressed air storage.

3. What factors affect the transient behavior of an air-filled tank?

The transient behavior of an air-filled tank is influenced by several factors, including the initial conditions of the air inside the tank, the properties of the tank material, the rate of heat transfer, and any external changes in temperature or pressure.

4. How is transient analysis of an air-filled tank performed?

Transient analysis is typically done using mathematical equations and computer simulations. These methods allow us to model and predict the behavior of the air inside the tank over time, based on the initial conditions and other factors mentioned above.

5. What are the applications of transient analysis in the study of air-filled tanks?

Transient analysis has various practical applications, including designing efficient HVAC systems, optimizing compressed air storage, and predicting the performance of air-filled tanks in different environments. It is also used in the study of natural phenomena, such as weather patterns and ocean currents, which involve the movement of air and other fluids.

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