Thermodynamics-Two Insulated Tank System

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Discussion Overview

The discussion revolves around a thermodynamics problem involving two insulated tanks filled with air at different pressures and the determination of final temperatures after mass equalization. The scope includes theoretical analysis and mathematical reasoning related to thermodynamic principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Participants calculate the initial masses in both tanks using the ideal gas law (PV=mRT), finding 18.24 kg in tank 1 and 182.4 kg in tank 2, leading to a collective mass of 200.64 kg.
  • Some participants note that the final mass in both tanks will be equal at 100.32 kg, but express uncertainty about how to incorporate enthalpy into the final temperature calculations.
  • One participant emphasizes that it is the pressure in both tanks that will equalize, not the temperature, suggesting that the final temperatures will differ.
  • Another participant raises a concern about the assumption that air can be treated as diatomic and the necessity of using heat capacity equations for the calculations.
  • Discussion includes a suggestion from a professor about obtaining mass flow rates and using energy balances to find final temperatures, while also noting that pressure differences drive material transfer.
  • An equation involving internal energy and specific heat capacity is introduced, indicating a relationship between temperature changes and internal energy for ideal gases.

Areas of Agreement / Disagreement

Participants generally agree that the final pressures will equalize, but there is no consensus on how to accurately determine the final temperatures or the role of enthalpy in the calculations. Multiple competing views on the approach to the problem remain unresolved.

Contextual Notes

There are limitations regarding assumptions about the ideal gas behavior of air, the treatment of enthalpy, and the specific heat capacities involved. The discussion does not resolve these assumptions or the implications for the calculations.

Who May Find This Useful

This discussion may be useful for students studying thermodynamics, particularly those interested in gas behavior, energy balances, and problem-solving in insulated systems.

mpn17
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Homework Statement



Two large, well-insulated tanks of 2m diameter and 5m in height are filled with air. One tank is initially at 1bar and 300oK and the other is at 10bar at 300oK. Determine the final temperature in both tanks if a valve connecting the two tanks is opened and the mass equalized (mf1=mf2) very quickly then closed again. Assume the enthalpy of the inlet and exit air for each tank is constant at 300.19kJ/kg. (Hint: One tank is ~198oK higher than the other after the valve shuts)

Homework Equations



PV=mRT
H=U+PV=U+RT


The Attempt at a Solution



I've used PV=mRT for both tanks to find the mass in tank 1 is 18.24kg while the mass in tank 2 is 182.4 kg. This gives a collective mass of 200.64kg. As stated in the problem statement the final mass in both tanks is equal which would then be 100.32 kg. From there I am not quite sure how to incorporate enthalpy into finding the final temperature in each tank?
 
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mpn17 said:

Homework Statement



Two large, well-insulated tanks of 2m diameter and 5m in height are filled with air. One tank is initially at 1bar and 300oK and the other is at 10bar at 300oK. Determine the final temperature in both tanks if a valve connecting the two tanks is opened and the mass equalized (mf1=mf2) very quickly then closed again. Assume the enthalpy of the inlet and exit air for each tank is constant at 300.19kJ/kg. (Hint: One tank is ~198oK higher than the other after the valve shuts)

Homework Equations



PV=mRT
H=U+PV=U+RT


The Attempt at a Solution



I've used PV=mRT for both tanks to find the mass in tank 1 is 18.24kg while the mass in tank 2 is 182.4 kg. This gives a collective mass of 200.64kg. As stated in the problem statement the final mass in both tanks is equal which would then be 100.32 kg. From there I am not quite sure how to incorporate enthalpy into finding the final temperature in each tank?

(1) It is not the mass, but the pressure in both tanks that will be equal at the end of the operation. Remember that the temperature will be different in each of the tanks.

(2) I cannot see how to do this calculation without assuming that air is (to a good approximation) made up of diatomic molecules, and introducing the heat capacity equation.
 
my professor mentioned being able to obtain the mass flow rate from the problem statement and then using an energy balance to then find the final temperature in each tank. He also said the pressure is not equal in both tanks.
 
mpn17 said:
my professor mentioned being able to obtain the mass flow rate from the problem statement and then using an energy balance to then find the final temperature in each tank. He also said the pressure is not equal in both tanks.

An interesting idea, and I am not convinced that it is a correct one. A pressure difference is a plausible driving force for transfer of material to equalize pressures while the tap is open; a mass difference is not.
 
H=U+PV
Given P,V,H
U only depends on the temperature assuming Ideal Gas Model
U=Cv(T2-T1)
((H-PV)/Cv)+T1=T2
Cv=Specific Temp of air (volume)
 

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