Advanced Thermodynamics in Mechanical Plants
Focused on concepts, equations, and practical applications for engineers and technicians
1. Overview
| Aspect |
Description |
| Purpose |
Optimize energy conversion, improve plant efficiency, and ensure safe operation of high‑temperature/pressure equipment. |
| Key Areas |
1. Real‑gas behavior 2. Irreversibility & entropy generation 3. Exergy analysis 4. Multi‑stage cycles 5. Heat‑transfer augmentation |
| Typical Systems |
Gas turbines, combined‑cycle plants, steam power plants, refrigeration/heat‑pump loops, cogeneration (CHP) units. |
2. Fundamental Relations (Re‑examined)
| Relation |
Symbol |
Typical Form (per unit mass) |
Remarks |
| First Law (Energy balance) |
Δe = q – w |
Δu + Δke + Δpe = q – w |
Include kinetic & potential terms for high‑speed flows. |
| Second Law (Entropy) |
Δs = ∫δq_rev/T + s_gen |
Δs = q/T_b + s_gen (for constant‑T heat addition) |
s_gen ≥ 0; zero for reversible processes. |
| Enthalpy–Entropy (h‑s) diagram |
– |
Useful for visualizing turbine/ compressor stages. |
|
| Gibbs Equation |
T ds = du + p dv – μ dN |
Links property changes to measurable variables. |
|
3. Real‑Gas Thermodynamics
3.1 Equations of State (EOS)
| EOS |
Equation |
Typical Use |
| Peng–Robinson |
(p = \frac{RT}{v-b} - \frac{a\alpha}{v(v+b)+b(v-b)}) |
Hydrocarbon pipelines, refrigerants. |
| Redlich‑Kwong |
(p = \frac{RT}{v-b} - \frac{a}{\sqrt{T},v(v+b)}) |
High‑temperature gas turbines. |
| Virial |
(Z = 1 + \frac{B(T)}{v} + \frac{C(T)}{v^2}+…) |
Low‑pressure steam and combustion gases. |
Implementation tip: Use tabulated departure functions to convert ideal‑gas properties → real‑gas properties.
3.2 Compressibility Factor (Z)
- Z = pv/RT; deviation from 1 indicates non‑ideal behavior.
- For design of compressors/turbines, compute Z at inlet/outlet to correct work and heat‑transfer calculations.
4. Irreversibility & Entropy Generation
4.1 Sources of Entropy Generation
- Heat transfer across finite ΔT
[
\dot{S}{gen}^{;heat}= \dot{Q}\left(\frac{1}{T{c}}-\frac{1}{T_{h}}\right)
]
- Fluid friction (pressure drop)
[
\dot{S}{gen}^{;fric}= \frac{\dot{W}{\text{loss}}}{T_{\text{avg}}}
]
- Mixing of streams with different T, p, composition
- Chemical reactions (combustion)
4.2 Minimization Strategies