Availability and Irreversibility

What is Meant by Availability and Irreversibility?

In thermodynamics, availability and irreversibility are closely related. Irreversible processes inevitably lead to a decrease in the availability of energy, as some of the energy that enters the system is inevitably lost as waste heat. This limits the efficiency of energy conversion processes, as some of the energy that could be used to do useful work is lost. Conversely, reversible processes are characterized by zero irreversibility and maximum availability, meaning that all the energy that enters the system can be used to do work. The concept of availability was first introduced by the physicist and mathematician Lord Kelvin in the mid-19th century as a measure of the maximum amount of work that could be extracted from a given system.

Since then, it has become a key concept in thermodynamics, used to evaluate the efficiency of energy conversion processes in a wide range of fields, from engineering and physics to environmental science and economics. Despite its importance, the concept of availability is often misunderstood or misapplied. Many people assume that availability is equivalent to energy, or that it is a measure of the total amount of work that can be extracted from a system. In reality, availability is a much more complex concept that takes into account factors such as temperature, pressure, and entropy, as well as the irreversibility of energy conversion processes. Understanding the relationship between availability and irreversibility is therefore essential for anyone seeking to design, optimize, or evaluate energy systems.

Formulas for GATE Mechanical Engineering – Fluid Mechanics and Machinery

What is Availability?

Availability is a fundamental concept in thermodynamics that measures the maximum amount of useful work that can be extracted from a system as it approaches a state of equilibrium with its surroundings. It is also known as exergy and is a measure of the quality of a system’s energy, as opposed to its total quantity. The availability of a system is determined by its state variables, such as temperature, pressure, and composition, as well as the availability of its surroundings, which includes both the external work that can be done and the heat that can be transferred.

The availability of a system is always less than its total energy, as some energy is lost as heat due to irreversibilities such as friction and heat transfer. In order to maximize the availability of a system, engineers and scientists seek to minimize these irreversibilities and optimize the design and operation of the system. This can lead to more efficient and cost-effective systems that have less environmental impact. When a system is subjected to a process from its original state to its dead state the maximum amount of useful work that can be achieved under ideal conditions is known as available energy or availability of the system.

W_max =AE = Q_xy – T₀(S_y-S_x)

Unavailable Energy: UAE = T₀(S_y-S_x)

where, S_x and S_yare the entropy at x and y, respectively.

Available Energy (AE) is also known as exergy and Unavailable Energy (UAE) as energy. Both forms of energy are important for the GATE ME exam. The energy which cannot be utilized for doing useful work is called unavailable energy. Irreversibility is equivalent to energy destroyed, hence also known as energy destruction consider the example given below.

Decrease in availability when Heat is transferred through finite temperature Difference

Consider a reversible heat engine operating between T₁ and T₀.

Q₁ = T₁. Δs

W = AE= (T₁ – T₀)Δs

Let us now consider heat Q₁ is transferred through a finite temperature difference.

Q₁ = T₁ Δs = T’₁ . Δs’

Δs’ > Δs

Q₂ = T₀ Δs → Initial UAE

Q’₂ = T₀ Δs’ ⇒ Afterward UAE

Q’₂ > Q₂

W’ =Q’₁ – Q’₂

W’ = T’₁ Δs’ – T₀Δs’

W’ = (T’₁ – T₀) Δs’

W = (T₁ – T₀) Δs

Formulas for GATE Mechanical Engineering – Machine Design

Second Law Efficiency

The second law efficiency is a measure of the efficiency of a thermodynamic system taking into account the irreversibilities that occur during the conversion of energy from one form to another. The second law of thermodynamics states that the total entropy of an isolated system always increases over time, which means that some energy is lost during any energy conversion process due to irreversibilities. The second law of efficiency is also known as the exergy efficiency or availability efficiency.

The second law of efficiency is different from the first law of efficiency, which only considers the quantity of energy that is the input and output of a system. The first law efficiency does not take into account the quality of the energy, which refers to how much of the energy can be converted into useful work. In contrast, the second law of efficiency considers the irreversibilities that occur during a thermodynamic process and quantifies the portion of the total energy that can be converted into useful work. The second law of efficiency is the ratio of the exergy recovered to the exergy spent. OR It is the ratio of actual work produced to the max work produced under reversible conditions. Consider the case of a heat engine.

The second law efficiency is a measure of the performance of a device relative to its performance under reversible conditions.

Exergy in Closed System

Exergy is a thermodynamic property that measures the maximum amount of useful work that can be extracted from a system as it approaches a state of thermodynamic equilibrium with its surroundings. In a closed system, the exergy is a measure of the maximum amount of useful work that can be obtained from the system if it were brought into thermodynamic equilibrium with its surroundings. The exergy of a closed system is also known as the available work or the maximum work.

The exergy of a closed system is determined by its state variables, such as temperature, pressure, and composition, and the state variables of its surroundings. The surroundings include the external work that can be done on the system and the heat that can be transferred between the system and its surroundings. The exergy of a closed system can be calculated using the first and second laws of thermodynamics.

Consider a piston-cylinder device that contains a fluid of mass m at temperature T and pressure P. The system is then allowed to undergo a differential change of state during which volume changes by dV and heat is transferred from the system to the surroundings.

For a change of exergy from state 1 to state 2.

Φ₁ = (E₁ – E₀) + P₀(V₁ – V₀) – T₀(S₁ – S₀)

Φ₂ = (E₂ – E₀) + P₀(V₂ – V₀) – T₀(S₂ – S₀)

Φ₁ – ϕ₂ = Energy at state 1 – Energy at state 2

Φ₁ – ϕ₂ = (E₁ – E₂) + P₀ (V₁ – V₂) – T₀(S₁ – S₂)

Exergy in Open System

Exergy is a concept in thermodynamics that refers to the maximum amount of useful work that can be obtained from a system or a process as it reaches equilibrium with its environment. When considering an open system, exergy takes into account both the energy and mass flow in and out of the system.

The exergy of an open system is calculated by subtracting the exergy of the incoming streams (i.e. energy and mass flows entering the system) from the exergy of the outgoing streams (i.e. energy and mass flows leaving the system), accounting for any changes in the system’s internal energy, as well as any work done by or on the system. A flowing fluid has an additional form of energy, called flow energy, which is the energy needed to maintain flow in a Pipe.

W_flow = PV

Exergy associated with the system is

Φ_{flowing fluid} = ϕ_{non flow fluid} + ϕ_flow

Φ_{flowing fluid} = (E₁ – E₀) + P₀(V₁ – V₀) – T₀(S₁ – S₀) +P₁V₁ – P₀V₀

Φ_flowing= U₁– U₀ + (KE)₁ – (KE)₀ + (PE)₁ – (PE)₀ + P₁V₁ – P₀V₀ – T₀ (S₁ – S₀)

Φ_{flowing fluid} = (U₁ + P₁V₁) – (U₀ + P₀V₀) – T₀(S₁ – S₀) + (KE)₁ – (KE)₀ + (PE)₁ – (PE)₀

Φ_flowing = (H₁ – H₀) – T₀ (S₁ – S₀) + (KE)₁ – (KE)₀ + (PE)₁ – (PE)₂

Important GATE Notes
I.C. Engines	Boiling
Turbomachinery	Pure Substances
Metal Cutting	Unsteady State Heat Transfer
Properties of Pure Substances	Steady State Heat Transfer
Free Convection	Forced Covection
First Law of Thermodynamics	Types of Support

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