To change the volume of a gas isothermally by a factor (f_{1}) of its initial value, it
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To change the volume of a gas isothermally by a factor \(f_{1}\) of its initial value, it is necessary to do work \(W_{1}\) on the gas. What work \(W_{2}\) is needed to change the volume by a factor \(f_{2}\) of the initial gas volume at the same temperature? Express your answer in terms of \(f_{1}, f_{2}\), and \(W_{1}\).
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