Yes for Same transformation from stage 1 (P1,V1,T1) to Stage 2 (P2,V2, T2), work required will be differed depends on by which process this transformation happened. Process followed is adiabatic, isentropic etc will have different amount of work.
By 1st Law of thermodynamics, Change in heat = Change in Internal energy+Work
For Two same stages, Change in internal energy will be same, its independent of transformation process which is taken to move from Stage 1 to Stage 2. Hence to accomodate different work, heat will be different for different processes.
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