When proving the equation,
why is dw= PdV not dw= PdV +vdP?
I think it is as you wrote, but don't quote me. I'm at school and dont have my book infront of me.
Work (force x distance) is done only if the pressure (force/area) acts over some change in volume (area x distance moved). If there is no change in volume, the force does not act over any distance - ie. the pressure just builds up but does not move anything (ie. it just increases internal energy). So, VdP is part of the internal energy of the gas, not the work done by the gas.
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