Compressing Gas: Work Done Calculation

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The discussion revolves around calculating the work done during the adiabatic compression of gas in a closed cylinder. The initial conditions are 1 bar pressure and 293K temperature, with a final volume of 1m3 and pressure of 10 bar. Participants note that the problem is under-defined due to the unknown gas type and its heat capacity ratio (γ). Assuming the gas is air with γ=1.4 allows for a solution using the ideal gas equation and work formula for adiabatic processes. The thread concludes with the assumption that the gas is air, leading to a resolution of the problem.
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Homework Statement


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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


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

The Attempt at a Solution


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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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