Questions: First Law for Open Systems and Control Volumes

Question 1

Why does enthalpy h = u + Pv appear in the steady-flow energy equation for open systems instead of internal energy u alone?

• A. Enthalpy is easier to look up in steam tables than internal energy
• B. Fluid crossing the control volume boundary must do flow work Pv to push against boundary pressure, so total energy transported per unit mass is u + Pv = h
• C. The pressure and volume terms cancel with each other in the derivation, leaving only u
• D. Enthalpy replaces internal energy only for incompressible liquids

Answer: (B)

Each parcel of fluid entering a control volume carries internal energy u but also does work Pv pushing the fluid column behind it across the boundary (flow work). Similarly, fluid leaving does flow work on what follows it. The total energy transported per unit mass is therefore u + Pv = h. This is a fundamental consequence of the open-system formulation, not merely a convenience.

Question 2

For any steady-flow device, the kinetic and potential energy terms in the energy equation can generally be safely neglected.

• T. True
• F. False

Answer: False

Kinetic and potential energy terms are often small compared to enthalpy and heat/work terms in turbines and compressors, and neglecting them is a reasonable approximation there. But for nozzles and diffusers — designed specifically to convert enthalpy to kinetic energy or vice versa — the kinetic energy change is the entire point and cannot be neglected. Similarly, large elevation changes in hydraulic turbines make the potential energy term significant.

Question 3

At steady state, what is the rate of change of energy stored inside a control volume, and what does this imply about the energy balance?

Model answer: At steady state, dE_cv/dt = 0 — the energy stored inside the control volume does not change with time. This means energy in (via mass flow and heat transfer) exactly equals energy out (via mass flow and work output), reducing the first law to a balance of boundary flows rather than a storage equation.

The full open-system first law is dE_cv/dt = Q̇ − Ẇ + Σ(ṁh)_in − Σ(ṁh)_out. Setting dE_cv/dt = 0 for steady state eliminates the storage term and yields Q̇ − Ẇ = Σ(ṁh)_out − Σ(ṁh)_in (plus kinetic and potential terms). This steady-flow energy equation is the working tool for analyzing turbines, compressors, heat exchangers, and nozzles.