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

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SUMMARY

The calculation of turbine work can be approached using two distinct methods: the first law of thermodynamics and the equation Q - W = U2 - U1. The first law is represented as -W = H2 - H1, leading to W = H1 - H2 = Cp(T1 - T2). Alternatively, the equation Q - W = U2 - U1 can yield W = U1 - U2 = Cv(T1 - T2), which may result in different outcomes. The discussion highlights that the application of Q - W = dU is specifically relevant for closed systems, suggesting a need for clarity in understanding these thermodynamic principles, especially in the context of polytropic processes.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Familiarity with enthalpy (H) and internal energy (U) concepts
  • Knowledge of specific heat capacities (Cp and Cv)
  • Basic principles of polytropic processes
NEXT STEPS
  • Study the application of the first law of thermodynamics in open systems
  • Explore the differences between Cp and Cv in thermodynamic calculations
  • Investigate polytropic processes and their implications in turbine work
  • Learn about closed versus open systems in thermodynamics
USEFUL FOR

Mechanical engineers, thermodynamics students, and professionals involved in energy systems and turbine design will benefit from this discussion.

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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