Exergy Analysis火用（可用能）分析

What you'll be able to do本章學習成果

• Explain the exergy reference environment, the dead state, exergy transfer, and exergy destruction.
• Evaluate exergy at a state and the change between states.
• Apply exergy balances to closed systems and control volumes at steady state.
• Define and evaluate exergetic efficiencies, and apply exergy costing.

Key equations重要公式

The idea of exergy火用的概念

Burn a small container of fuel in an abundant atmosphere and you end with a slightly warm mixture. By the first law, the energy is unchanged. Yet the initial fuel–air combination could have generated electricity or driven a car, while the final warm mixture can do essentially nothing. The potential for use was destroyed by the irreversible combustion. Exergy is the property that quantifies that potential — and it is exergy, not energy, that has economic value.

Environment & dead state環境與死態

Exergy is defined relative to a model of the surroundings. The exergy reference environment is a large, uniform simple compressible system at fixed $p_0$ and $T_0$ (typically 1 bar, 25 °C). A system reaches the dead state when it is at $T_0, p_0$ and at rest relative to the environment — no temperature, pressure, or motion difference remains, so no work can be extracted. Exergy is the maximum theoretical work obtainable as the system passes to the dead state.

Defining exergy火用的定義

Combining energy and entropy balances for a system coming to equilibrium with the environment gives:

Once the environment is fixed, this depends only on the system's properties — so exergy is itself an extensive property. It is zero at the dead state, positive everywhere else, and never negative. (This thermomechanical exergy ignores composition differences; the chemical exergy of fuels comes later.)

The exergy balance火用平衡

Like entropy, exergy is transferred across boundaries but is not conserved — irreversibilities destroy it. For a closed system at steady state:

The destruction term is tied directly to entropy production: $\dot E_d = T_0\,\dot\sigma \ge 0$. This is the bridge from the second law to "lost work" measured in kilowatts.

Exergy of heat transfer熱傳的火用

Heat carries exergy, but only the fraction set by the Carnot factor at the temperature where it crosses the boundary:

So the same heat rate is worth far more at high temperature than at low. When heat is conducted across a finite temperature drop — say from a 600 K source to a 310 K surface, with $T_0 = 300$ K — the exergy entering ($50$ kW for $\dot Q = 100$ kW) far exceeds the exergy leaving ($3$ kW). The difference, 47 kW, is destroyed inside the irreversible conduction. Energy passed through untouched; usefulness was largely annihilated.

Exergy-destruction lab火用損毀實驗室

Conduct heat from a hot source to a lower use temperature. The top bar shows energy (fully conserved); the bottom bars show exergy splitting into the part actually delivered and the part destroyed by the temperature drop. Squeeze the gap between $T_1$ and $T_2$ and watch destruction shrink — the case for matching source and use temperatures.

Flow exergy & control volumes流動火用與控制體積

For streams crossing a control surface, the specific flow exergy parallels enthalpy's role in the energy balance:

The steady-state control-volume exergy balance then reads $0 = \sum(1-T_0/T_j)\dot Q_j - \dot W_{cv} + \dot m(e_{f1}-e_{f2}) - \dot E_d$, letting us locate destruction component-by-component.

Exergetic efficiency火用效率

An exergetic efficiency compares useful exergy output to exergy input — a truer measure than energy efficiency. A counterflow heat exchanger can be 100% energy-efficient (no heat lost) yet only ~40% exergy-efficient, because stream-to-stream heat transfer across a finite gap destroys exergy. For fuel-fired heating, the exergetic efficiency can be under 10% — a thermodynamically poor match between a flame's high source temperature and a low use temperature, even when the energy efficiency looks excellent.

Exergy of a heat transfer熱傳的火用