Lesson 7.3: Entropy & Availability

Entropy and availability are key concepts in thermodynamics that help determine energy quality, irreversibility, and maximum work. GATE and PSU exams frequently test entropy change calculations and availability analysis.

🔹 1. Introduction

• Entropy (S): Measure of disorder or unavailability of energy for work

• Availability / Exergy (ψ): Maximum useful work obtainable from a system as it reaches equilibrium with surroundings

• Applications: Power plants, refrigeration, energy efficiency analysis, feasibility studies

🔹 2. Entropy

• Definition:

dS=dQrevTdS = \frac{dQ_\text{rev}}{T}dS=TdQrev​​

• Properties:

  1. Entropy is a state function

  2. For reversible processes: ΔS = Q/T

  3. For irreversible processes: ΔS > Q/T

• Entropy Change Examples:

  • Isothermal process: ΔS = Q/T

  • Adiabatic reversible process: ΔS = 0

  • Mixing of two fluids → entropy increases

• Second Law Relation: Entropy of isolated system never decreases

🔹 3. Availability / Exergy

• Definition: Maximum work obtainable from a system relative to the environment

• Formula:

ψ=(U+P0V−T0S)+KE+PE\psi = (U + P_0 V – T_0 S) + KE + PEψ=(U+P0​V−T0​S)+KE+PE

Where U = internal energy, V = volume, S = entropy, P₀, T₀ = environmental pressure and temperature

• Exergy Destruction:

ψlost=T0ΔSgen\psi_\text{lost} = T_0 \Delta S_\text{gen}ψlost​=T0​ΔSgen​

• Applications: Evaluate efficiency of turbines, engines, heat exchangers

🔹 4. Solved Examples (PYQ Style)

1. Calculate entropy change for isothermal expansion of ideal gas

2. Determine entropy generation in irreversible adiabatic process

3. Compute maximum work (availability) for system exchanging heat with environment

4. Analyze exergy destruction in turbine and refrigeration cycles

🔹 5. Practice Exercises

1. Calculate ΔS for heating and cooling processes

2. Determine entropy change for mixing of two fluids

3. Compute exergy for heat transfer process at given T₀

4. Solve problems on availability of steam in turbine

5. Analyze irreversibility in engineering processes

🔹 6. Summary

• Entropy (S): Measure of disorder; state function; increases in irreversible processes

• Availability / Exergy (ψ): Maximum useful work obtainable; reduced by irreversibility

• Applications: Energy efficiency, turbines, engines, power and refrigeration cycles

• Importance in Exams: Questions on ΔS, ψ, and exergy losses are common in GATE & PSU