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

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Turbine work can be calculated using both the first law of thermodynamics and the equation Q - W = U2 - U1, but they apply in different contexts. The first law approach, W = H1 - H2, is commonly used, leading to W = Cp(T1 - T2). In contrast, using Q - W = U2 - U1 suggests W = U1 - U2, which could yield different results, particularly if Cv is used instead of Cp. The confusion may stem from the applicability of these equations, as Q - W = dU is typically relevant for closed systems. Understanding the context of each equation is crucial for accurate calculations in thermodynamic processes.
kal00
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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.
 
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Something in my head clicked and I'm guessing the Q - W = dU is only for closed systems?
 
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