Question

The final volume of a system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?

Answer 1

Explanation:

System-led function is neither strictly zero nor necessarily non zero.  

If the pressure P remains constant in a given cycle, then

$\\ \Delta W=P \Delta V \\ W=P\left(V_{2}-V_{1}\right) \\ V_{2}=V_{1} \\ W=0 \\ V_{1}=V_{2} \\ V_{1} is initial volume\\ \mathrm{V}_{2} is Final volume$

It is, then, an isobaric operation.

Even if $\mathrm{P}=\mathrm{P}(\mathrm{V}), \text { if } \mathrm{V}_{2}=\mathrm{V}_{1}$, the net work performed will be zero. Work done in this situation is zero.  

If the system is going through a cyclic phase, then after one cycle the initial volume is equal to the final volume. Yet gas-led research is non-zero.