Steady-Flow Processes in Thermodynamics – Identify the Invariant Quantity For a steady-flow process through a control volume (e.g., nozzle, turbine, heat exchanger), properties at fixed locations do not change with time. In particular, the mass flow rate entering equals the mass flow rate leaving when the control volume mass is steady.

Introduction / Context:
Steady-flow analysis underpins the design of turbines, compressors, nozzles, and heat exchangers. The concept of “steady” means that at any fixed point in the device, intensive properties and flow variables do not change with time, enabling averaged energy and mass balances.

Given Data / Assumptions:

• Control volume with steady operation (no net accumulation of mass over time).
• Single or multiple inlets/outlets possible.
• Transient start-up/shutdown excluded from the definition of steady state.

Concept / Approach:

For steady flow, the mass conservation statement is m_dot_in = m_dot_out when the control-volume mass remains constant. Heat and work rates can be time-dependent in practice (e.g., changing load), yet the process can still be steady if properties at a point do not vary with time. Therefore, the safest invariant to pick from the options is mass flow balance, not necessarily constant heat or work rates.

Step-by-Step Solution:

Verification / Alternative check:

Plant data logs often show small fluctuations in heat or shaft power during “steady” operation, while flow and state variables remain effectively constant—confirming that strict constancy of Q_dot or W_dot is not required by the definition.

Why Other Options Are Wrong:

Heat/work transfer rates need not be constant to qualify as steady; enthalpy can change between inlet and outlet (e.g., across heaters or turbines), so it is not invariant either.

Common Pitfalls:

Equating “steady” with “constant everything”; forgetting that steady is about time invariance at a location, not equality of inlet and outlet properties except for conserved totals like mass.

Final Answer:

mass flow at inlet and outlet is same