Steady-state material balance:\r In a steady-state system (no net accumulation with time), the rate of material __________ equals zero.

Introduction:
Material balance is the foundation of process analysis. The general balance states: accumulation = input − output + generation − consumption. At steady state, system properties are time-invariant, simplifying many calculations in reactors, separators, and networks.

Given Data / Assumptions:

• System is at steady state (d/dt of inventories = 0).
• Generation/consumption terms may exist (e.g., reaction), but are constant over time.
• Boundary flows (input/output) are constant in time.

Concept / Approach:
Steady state means no net change in the amount of material inside the system with time. Therefore, the accumulation term is zero, even though generation and consumption can be nonzero and must be balanced by appropriate differences between input and output. Confusing “generation” with “accumulation” is common; generation refers to formation within the system (e.g., reaction), while accumulation is the net time rate of increase of inventory.

Step-by-Step Solution:
Write general balance: accumulation = input − output + generation − consumption.At steady state: accumulation = 0 by definition.Conclude that only the accumulation term is guaranteed zero; others can be nonzero.

Verification / Alternative check:
In continuous stirred-tank reactors at steady state with reaction, generation is balanced by a higher output relative to input, keeping accumulation zero.

Why Other Options Are Wrong:

• Production/generation may be nonzero due to reaction.
• Input is generally not zero in continuous operation.
• Consumption can be nonzero due to reaction or sorption.

Common Pitfalls:
Setting generation to zero at steady state; that only applies to nonreactive systems.

Final Answer:
accumulation