Last reviewed 4 Nov 2026 · 3 min read
1. Degrees of freedom in process calculations
FormulaDegrees of freedom
| Value | Meaning |
|---|---|
| N_DF = 0 | Exactly specified — the problem can be solved |
| N_DF > 0 | Under-specified — more data (or specifications) needed |
| N_DF < 0 | Over-specified — too many data; possibly inconsistent |
Independent equations available
- Material balances — at most one per independent component (for a non-reactive process, the number of components); with reactions, use molecular-species balances with extent of reaction, or atom balances.
- Energy balance (if energy terms are unknown).
- Process specifications — e.g. "conversion is 80%", "split ratio 1:3".
- Physical properties and laws — e.g. phase equilibrium (Raoult's law), density relations.
- Physical constraints — mole fractions in a stream add to 1.
Worked Example1 — A mixer
Two streams of benzene–toluene mixture are mixed. Stream 1: 100 mol/h, 40% benzene; Stream 2: unknown flow, 70% benzene; product: unknown flow, 60% benzene. Unknowns: flow of stream 2 and product → 2. Independent balances: benzene and toluene (or total) → 2. → solvable. Benzene: mol/h; product = 300 mol/h.
- For multi-unit processes, do a degrees-of-freedom count for each unit and for the overall system, and start with a unit (or the overall balance) that has N_DF = 0.