Does the volume of a thermodynamic system always have to change for it to do work? If yes,could you explain why? And if no, could you provide the example of a system, where it is not neccesary.
Answer
Yes, because work is force times distance moved. It's not immediately obvious that this means work can only be done if the volume changes, but have a look at How much work is needed to compress a certain volume of gas? where I went into this in some detail. If any parts of this aren't clear comment here and I can go into them in more detail.
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