Is Turbine Work Calculated Using the First Law or Q - W = U2 - U1?

[kal00]

So I'm just a little confused with turbine work.

Generally I've been solving it with first law -W = H2 - H1, so W = H1 - H2 = Cp(T1 - T2)

But what about Q - W = U2 - U1?

Can't that make it W = U1 - U2 = Cv(T1 - T2) giving a different answer. I have a feeling my understanding of something is amiss.

 

[kal00]

Something in my head clicked and I'm guessing the Q - W = dU is only for closed systems?

 

[jack action]

Does this explanation from the point of view of a polytropic process helps you?