Compressing Gas: Work Done Calculation

[bassguitar]

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
pV^y = 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?

 

[Chestermiller]

Do you know what gas is, or whether it is mono atomic?

 

[BvU]

Hello BassGuitar,

Can't you use the ideal gas equation twice ?

[edit] never mind. Leave this to Chet !

 

[bassguitar]

Unfortunately, the gas type is not mentioned :(

 

[Chestermiller]

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 $\gamma=1.4$

 

[bassguitar]

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.