A thermodynamic system goes from states
\[
\text{i)}\quad (P,V)\ \rightarrow\ (P,2V)
\]
\[
\text{ii)}\quad (P_1,V)\ \rightarrow\ (2P_1,V)
\]
Then the works done in these two cases are
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Remember:
\[
\text{Isobaric process: }
W=P\Delta V
\]
and
\[
\text{Isochoric process: }
W=0.
\]
No volume change means no work done by the gas.