What is entropy balance, and how is it applied?

Short Answer:

Entropy balance is a method used in thermodynamics to calculate the change in entropy of a system by considering all the entropy entering, leaving, and generated within the system. It helps in analyzing how entropy behaves during a process and whether the process is reversible or irreversible.

Entropy balance is applied in thermal systems like heat exchangers, compressors, turbines, and refrigerators to check how much entropy is added by heat transfer, how much is removed, and how much is generated due to irreversibilities. It is very useful in designing efficient and reliable energy systems.

Detailed Explanation:

Entropy balance and its application

In thermodynamics, energy balance tells us how much energy enters and leaves a system. Similarly, entropy balance helps track how entropy flows and changes in a system during any process. Since entropy is related to energy quality and disorder, using entropy balance allows engineers to analyze efficiency, irreversibility, and performance of real processes.

Entropy balance follows the Second Law of Thermodynamics, which states that entropy in an isolated system can never decrease. In practical systems, entropy can enter or leave with heat and mass, and can also be generated internally due to friction, mixing, or heat transfer through a temperature difference.

General Entropy Balance Equation

For a closed system, the entropy balance is written as:

ΔS_system = ∑(Entropy in) – ∑(Entropy out) + S_generated

Where:

  • ΔS_system = change in entropy of the system
  • Entropy in/out = due to heat transfer or mass flow
  • S_generated = entropy produced inside the system (always ≥ 0)

If the process is reversible, then S_generated = 0.
If the process is irreversible, then S_generated > 0.

Application in Thermodynamic Systems

Entropy balance is applied in many thermal systems. Let us look at some common applications:

  1. Heat Exchangers

In heat exchangers, hot and cold fluids exchange heat. Entropy balance is used to:

  • Calculate entropy change in both fluids
  • Find entropy generation due to temperature differences
  • Optimize heat exchanger design to reduce irreversibility

Goal: Improve heat transfer with minimum entropy generation.

  1. Turbines and Compressors

In turbines, high-pressure steam or gas expands and does work. Entropy balance is applied to:

  • Analyze the entropy increase due to fluid friction
  • Estimate how far the process is from isentropic (ideal)
  • Improve blade design and flow path

Goal: Maximize work output by minimizing entropy generation.

  1. Refrigerators and Heat Pumps

In refrigerators, entropy balance helps:

  • Track entropy carried away from the cooled space
  • Account for entropy added due to compressor heat
  • Calculate coefficient of performance (COP)

Goal: Ensure efficient cooling with less energy loss.

  1. Combustion Chambers

In engines and boilers, combustion produces heat and gases. Entropy balance:

  • Helps in calculating entropy change of gases
  • Measures how much of the heat becomes unusable
  • Analyzes environmental impact due to entropy rise

Goal: Use fuels more efficiently and reduce waste heat.

  1. Closed System Analysis

In piston-cylinder setups, the working fluid is compressed or expanded. Entropy balance helps:

  • Track entropy change during compression or expansion
  • Compare with isentropic (ideal) processes
  • Understand losses due to friction or heat leakage

Goal: Increase cycle efficiency (e.g., in Otto or Rankine cycles)

Why Entropy Balance is Important

  • Detects Irreversibility: Shows how much energy is lost in the form of disorder.
  • Design Improvement: Helps in redesigning systems to reduce entropy generation.
  • Efficiency Calculation: Indicates how close a system is to ideal operation.
  • Environment-Friendly: Helps reduce energy waste and pollution.
  • Supports Second Law: Confirms if the process follows the second law properly.
Conclusion

Entropy balance is a powerful tool used to analyze how entropy enters, leaves, and is generated within a thermodynamic system. It helps engineers understand system losses, identify inefficiencies, and improve the design of energy-converting machines. By applying entropy balance to systems like turbines, heat exchangers, and refrigerators, one can ensure better energy utilization, lower waste, and higher performance.