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 non-zero.
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Answer
Work done by the system is neither necessarily zero nor necessarily non-zero.
If in a certain process, the pressure P stays constant, then,
$\Delta\text{W}=\text{P}\Delta\text{V}$
$\Rightarrow\text{W}=\text{P}(\text{V}_2-\text{V}_1)$
As $\text{V}_2=\text{V}_1$
$\Rightarrow\text{W}=0$
(Initial volume, V1 = Final volume, V2)
Hence, it is an isobaric process.
Even if P = P(V), net work done will be zero if V2 = V1. In this case, work done is zero.
If the system goes through a cyclic process, then initial volume gets equal to the final volume after one cycle. But work done by the gas is non-zero.
If in a certain process, the pressure P stays constant, then,
$\Delta\text{W}=\text{P}\Delta\text{V}$
$\Rightarrow\text{W}=\text{P}(\text{V}_2-\text{V}_1)$
As $\text{V}_2=\text{V}_1$
$\Rightarrow\text{W}=0$
(Initial volume, V1 = Final volume, V2)
Hence, it is an isobaric process.
Even if P = P(V), net work done will be zero if V2 = V1. In this case, work done is zero.
If the system goes through a cyclic process, then initial volume gets equal to the final volume after one cycle. But work done by the gas is non-zero.
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