Exergy Analysis

Why it matters

Exergy analysis is crucial for understanding the efficiency of energy conversion processes and identifying where improvements can be made. It helps engineers design systems that minimize energy waste and optimize performance, which is essential in industries like power generation, refrigeration, and chemical processing.

Key ideas

• Exergy: The maximum useful work possible during a process that brings the system reversibly into equilibrium with a specified environment, accounting for the available thermal, mechanical and, where relevant, chemical differences.
• Dead State: A state where the system is in equilibrium with its surroundings, having no potential to do work.
• Exergy Destruction: Represents the loss of potential to do work due to irreversibilities in the process.
• Exergy Efficiency: A measure of how efficiently a system converts available energy into useful work.
• Exergy Balance: Similar to energy balance but accounts for the quality of energy.

Formulas

• Ex = (U - U0) + P0(V - V0) - T0(S - S0)

  • Ex: Exergy (Joules)
  • U: Internal energy (Joules)
  • U0: Internal energy at dead state (Joules)
  • P0: Ambient pressure (Pascals)
  • V: Volume (cubic meters)
  • V0: Volume at dead state (cubic meters)
  • T0: Ambient temperature (Kelvin)
  • S: Entropy (Joules per Kelvin)
  • S0: Entropy at dead state (Joules per Kelvin)

• Ex_destruction = T0 * S_gen

  • Ex_destruction: Exergy destruction (Joules)
  • S_gen: Entropy generation (Joules per Kelvin)

• Ex_efficiency = (Ex_output / Ex_input) * 100

  • Ex_efficiency: Exergy efficiency (percentage)
  • Ex_output: Exergy output (Joules)
  • Ex_input: Exergy input (Joules)

The displayed nonflow physical-exergy expression neglects kinetic, potential and chemical exergy and uses the same system mass/composition at the environmental reference state. Flow physical exergy per mass instead uses (h-h₀)-T₀(s-s₀), plus kinetic/potential contributions where relevant. Exergy efficiency must define the desired product and the exergy expended, rather than counting all waste output as useful.

Worked example

Given consistent property values for a physical-exergy bookkeeping exercise, with kinetic, potential and chemical contributions excluded:

• A system with internal energy U = 5000 J
• Volume V = 0.1 m³
• Entropy S = 20 J/K
• Ambient conditions: P0 = 101325 Pa, T0 = 300 K, U0 = 4000 J, V0 = 0.08 m³, S0 = 15 J/K

Steps:

1. Calculate the exergy using the formula: Ex = (U - U0) + P0(V - V0) - T0(S - S0) Ex = (5000 J - 4000 J) + 101325 Pa * (0.1 m³ - 0.08 m³) - 300 K * (20 J/K - 15 J/K) Ex = 1000 J + 2026.5 J - 1500 J Ex = 1526.5 J

Final Answer: 1526.5 J

Common mistakes

• Confusing energy with exergy; remember that exergy accounts for energy quality.
• Ignoring the dead state conditions, which are crucial for accurate calculations.
• Miscalculating entropy changes, leading to incorrect exergy destruction values.

For GATE ME

• Focus on problems involving exergy balance and efficiency calculations.
• Practice identifying and calculating exergy destruction in various thermodynamic cycles.
• Understand the impact of irreversibilities on system performance.

Quick check

1. What is exergy?
2. How does exergy differ from energy?
3. Why is the dead state important in exergy analysis?

Answers: 1. Maximum useful work potential. 2. Exergy considers energy quality. 3. It defines the reference state for calculations.