Introduction to Material and Energy Balances
Fundamental concepts for chemical‑process, environmental, and mechanical engineering
| Reason | What It Shows |
|---|---|
| Design | Size of reactors, separators, heat exchangers, and utility systems |
| Safety | Limits of accumulation, pressure, temperature, and hazardous releases |
| Economics | Raw‑material costs, product yields, energy consumption, waste treatment |
| Environmental compliance | Emission limits, carbon‑footprint, life‑cycle analysis |
| Symbol | Meaning | Typical Units |
|---|---|---|
| ( \dot{n} ) | Molar flow rate | kmol · h⁻¹ |
| ( \dot{m} ) | Mass flow rate | kg · h⁻¹ |
| ( \dot{V} ) | Volumetric flow rate | m³ · h⁻¹ |
| ( F_i ) | General flow of component i (mass, mol, or vol) | |
| ( \dot{Q} ) | Heat transfer rate | kW |
| ( \dot{W} ) | Shaft work rate | kW |
| ( \Delta H ) | Enthalpy change | kJ · kmol⁻¹ |
| ( \Delta U ) | Internal‑energy change | kJ · kmol⁻¹ |
| ( \dot{E} ) | Total energy flow (heat + work + enthalpy) | kW |
For any conserved property ( \Phi ) (mass, species, energy, momentum) applied to a control volume (CV):
[ \boxed{\displaystyle \underbrace{\sum \dot{\Phi}{\text{in}}}{\text{inflow}} ;-; \underbrace{\sum \dot{\Phi}{\text{out}}}{\text{outflow}} ;+; \underbrace{\dot{\Phi}{\text{gen}}}{\text{generation}} ;=; \underbrace{\frac{d}{dt}!\left(\Phi_{\text{CV}}\right)}_{\text{accumulation}} } ]
[ \sum \dot{m}{\text{in}} - \sum \dot{m}{\text{out}} = \frac{dM_{\text{CV}}}{dt} ]
For component i:
[ \underbrace{\sum \dot{n}{i,\text{in}}}{\text{in}} - \underbrace{\sum \dot{n}{i,\text{out}}}{\text{out}} + \underbrace{r_i V}{\text{generation/consumption}} = \underbrace{\frac{d n_i}{dt}}{\text