Compressing Gas: Work Done Calculation

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    Compression Gas
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Discussion Overview

The discussion revolves around calculating the work done during the adiabatic compression of gas in a closed cylinder with a piston. Participants explore the implications of missing information about the type of gas and its properties, such as heat capacity.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes the initial conditions of the gas and the equations relevant to the problem, highlighting unknown variables such as T2, V1, and y.
  • Another participant questions whether the type of gas is known or if it is monoatomic, suggesting that this information is crucial for solving the problem.
  • A suggestion is made to use the ideal gas equation twice to find the necessary variables, although this is later dismissed by the same participant.
  • It is pointed out that without knowing the type of gas, specifically its heat capacity or ##\gamma##, the problem remains under-defined.
  • One participant proposes assuming the gas is air with ##\gamma=1.4##, indicating that this assumption could lead to a clear solution.
  • A later reply acknowledges the under-definition of the problem and expresses gratitude for the assistance, indicating a potential resolution based on the assumption of air.

Areas of Agreement / Disagreement

Participants generally agree that the lack of information about the gas type complicates the solution. However, there is no consensus on how to proceed without this information, and multiple views on assumptions remain present.

Contextual Notes

The discussion highlights limitations due to missing assumptions about the gas type and its properties, which are essential for applying the equations correctly. The dependence on the assumption of air as the gas type introduces uncertainty in the solution.

bassguitar
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Homework Statement


[/B]
A closed cylinder with a piston is used to compress gas that is initially at 1bar and temperature 293K. The compression is performed adiabatically until the volume is 1m3 and the pressure is 10bar, calculate the work done.

Homework Equations


[/B]
pV = nR0T - ideal gas assumption
pVy = const. - adiabatic compression
W = (p2V2 - p1V1) / y - 1 - work for adiabatic compression

The Attempt at a Solution


[/B]
We have the following unknown variables: T2 , V1 and y. And we only have two equations. Is there anything I am missing?
 
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Do you know what gas is, or whether it is mono atomic?
 
Hello BassGuitar, :welcome:

Can't you use the ideal gas equation twice ?

[edit] :smile: never mind. Leave this to Chet !
 
Unfortunately, the gas type is not mentioned :(
 
bassguitar said:
Unfortunately, the gas type is not mentioned :(
Well, you need to know the heat capacity, or equivalently, ##\gamma##. Suppose you assume that the gas is air, with ##\gamma=1.4##
 
Yes, so I guess the problem is under-defined. If I assume that the gas is air the solution is obvious. Thank you for your help. I will mark this as solved.
 

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