# Calculate the work w when 1 litre of an ideal gas at an initial pressure of 31 atm is expanded isothermally to a final volume of 31 litres into a vacuum.Im pretty sure the answer is 0 because its...

Calculate the work *w* when 1 litre of an ideal gas at an initial pressure of 31 atm is expanded isothermally to a final volume of 31 litres into a vacuum.

Im pretty sure the answer is 0 because its against a vacuum, but apparently it isnt!! can anyone help??

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### 1 Answer

Considering the change of volume is affected in a reversible manner, the work done will be non-zero. In that case w = nRT ln V2/V1 = nRT ln P1/P2 = nRT ln 31/1 (here, P2 is = 1, obtained from the isothermal condition P1V1=P2V2). But the way expansion is described in the problem, it seems to be done in a drastic (hence irreversible) manner, in which case w(irrev) = P ext. (V2-V1) = 0 (as it is expanding against a vacuum). In essence, a little bit of additional information would have been very helpful.

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