Calculating Heat Transfer in a Reversible Isothermal Process with a Slow Leak

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Discussion Overview

The discussion revolves around calculating heat transfer in a rigid tank during a reversible isothermal process where air seeps in through a small hole. Participants explore the implications of the problem's assumptions and the application of thermodynamic principles, particularly focusing on the first law of thermodynamics and the behavior of ideal gases.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the adequacy of the information provided to solve the problem, suggesting a need for further guidance.
  • Another participant advises considering the first law of thermodynamics and treating the air as an ideal gas.
  • A different participant questions the formula Q=T[S(2)-S(1)], suggesting a possible misunderstanding of the symbols used and proposing an alternative approach using the ideal gas law.
  • Another participant clarifies that S likely refers to entropy and discusses the application of the second law of thermodynamics in this context.
  • There is a mention of the assumption that kinetic and potential energies are negligible, and a suggestion to use a control volume approach for analysis.
  • A participant expresses gratitude for the assistance and shares their background, indicating a return to study after a long break and some confusion about basic concepts.
  • Questions arise regarding the determination of the state of a fluid given two properties (temperature and pressure) and which tables to use for reference.
  • One participant inquires about the methodology for applying a control volume in this scenario.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are multiple competing views on the appropriate methods and formulas to apply in solving the problem. Uncertainties regarding the interpretation of symbols and the application of thermodynamic principles are evident.

Contextual Notes

Limitations include potential misunderstandings of thermodynamic symbols and equations, as well as the need for clarification on the application of control volume analysis. The discussion reflects varying levels of familiarity with the subject matter among participants.

Who May Find This Useful

This discussion may be useful for students studying thermodynamics, particularly those grappling with concepts related to heat transfer, ideal gas behavior, and the application of the first and second laws of thermodynamics in practical scenarios.

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Homework Statement


Rigid tank volume .5m^3 initially evacuated. Tiny hole develops, air seeps in @ 1 bar and 21 degrees C. Pressure in tank reaches 1 bar, slow leak so temp remains 21 deg C inside tank. What's amount of heat transfer?


Homework Equations



Q=T[S(2)-S(1)]
Pv=nRT

The Attempt at a Solution



Ok, I understand this is a reversible isothermal process but it seems that I am not given enough information to solve the problem. Please help to send me in the right direction! Thanks!
 
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Have you taken a look at the the first law? You know of the assumptions for the problem, I would also add to treat the air as an ideal gas.
 
I'm very new to thermo but I haven't seen this formula Q=T[S(2)-S(1)], unless the S's means Volumes, I write it as capital V's

but anyways.. not the point... for rigid tanks, isn't the volume constant so you can solve for Q then use Q to find the missing variables in Pv=nRT

the temperature will give you the pressure, and you would have to treat this as an ideal gas, you're given little v, and I think you can get R from Q, or by the chartes... so then you just have P?

I havn't covered rigid tanks yet, so I'm probably very wrong...
 
The S probably stands for entropy. He probably got the first equation from the 2nd law of themo, S2 - S1 = Q/Tb + sigma, where sigma will equal zero since it's a reversible process.

PV =nRT works, but i think PV = mRT is a better variation of the ideal gas for this problem.

I'm guessing the others assumption that KE and PE are negligble. Take a control volume and you can see what you need to do from there.
 
Last edited:
thank you...

Thanks for the help - I appreciate the responses...have returned to school after a LONG break and some of the basics are pretty hazy

I thought that a control volume would only be applied to fluids?

By the S's I was meaning entropy, didn't know how to show using subscripts.

Side question - I know that when you are given two properties of a fluid (such as temperature and pressure) that you should know what state they are in (superheated etc)...but how exactly is that determined?
And, iff you are given both temp and press which table should you be using?
 
if I do need to do a control volume - how exactly do i do that?
 

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