Exergy: A measure of Work Potential Chapter 8

Work Potential of Energy When a new energy source is discovered, the first thing the explorers do is estimate the amount of energy contained in the source. Work Potential: is the amount of energy we can extract as useful work. The rest of the energy will eventually be discarded as waste energy and is not worthy of our consideration..

Exergy The property that enables us to determine the useful work potential of a given amount of energy at some specified state is exergy, which is also called the availability or available energy. Exergy is a property and is associated with the state of the system and the environment. The property exergy is also called availability or available energy.

Dead State: A system that is in equilibrium with its surroundings has zero exergy and is said to be at the date state. At the dead state, a system is at the temperature and pressure of its environment; it has no kinetic or potential energy relative to the environment.

Distinction shoud be made between the surroundings, immediate surroundings and the environment. Surrounding: are everything outside the system boundaries. Immediate surrounding: the portion of the surrounding that is affected by the process. Environment: the region beyond the immediate surroundings.

A system will deliver the maximum possible work as it undergoes a reversible process from the specified initial state to the state of its environment, that is, the dead state. The exergy of heat supplied by thermal energy reservoirs is equivalent to the work output of a Carnot heat engine operating between the reservoir and the environment.

Exergy (Work Potential) Associated with Kinetic and Potential Energy The work potential or exergy of the kinetic energy of a system is equal to the kinetic energy itself regardless of the temperature and pressure of the environment. The exergy of the potential energy of a system is equal to the potential energy itself regardless of the temperature and pressure of the environment.

Example 1: A windmill with 12 m diameter rotor as shown in fig Example 1: A windmill with 12 m diameter rotor as shown in fig. is to be installed at a location where the wind is blowing steadily at an average velocity of 10m/s. Determine the maximum power that can be generated by the windmill.

The work done by work-producing devices is not always entirely in a usable form. For example, when a gas in a piston-cylinder device expands, part of the work done by the gas is used to push the atmospheric air out of the way of the piston.

The difference between the actual work W and the surroundings work Wsurr is called useful work Wu: The work done Wsurr by or against the atmospheric pressure has significance only for systems whose volume changes during the process (i.e., systems that involve moving boundary work.)

Work done Wsurr by or against atmospheric pressure has no significance for cyclic devices and systems whose boundaries remain fixed during a process such as rigid tanks and steady-flow devices (turbines, compressors, nozzles, heat exchangers, etc.)

Reversible work Wrev. is defined as the maximum amount of useful work that can be produced as a system undergoes a process between the specified initial and final states. The useful work output obtained when the process between the initial and final states is executed in a totally reversible manner.

The difference between the reversible work Wrev and the useful work Wu is due to the irreversibilities present during the process and is called irreversibility I. It is equivalent to the exergy destroyed and is expressed as Where Sgen is the entropy generated during the process.

For a totally reversible process, the useful and reversible work terms are identical and thus exergy destruction is zero. Irreverisbility can be viewed as the wasted work potential or the lost opportunity to do work. The smaller the irreversibility associated with a process, the greater the work that will be produced. The performance of a system can be improved by minimizing the irreversibility associated with it.

Example: A heat engine receives heat from a source at 1200 K at a rate of 500 kJ/s and rejects the waste heat to a medium at 300 K. The power output of the heat engine is 180 kW. Determine the reversible power and the irreversibility rate for this process.

Example: A 500 kg iron block shown in fig Example: A 500 kg iron block shown in fig. is initially at 200OC and is allowed to cool to 27OC by transferring heat to the surrounding air at 27OC. Determine the reversible work and the irreversibility for this process.

Second-Law Efficiency The second-law efficiency is a measure of the performance under reversible conditions for the same end states and is given by For Heat engines and the work-producing devices

For refrigerators, heat pumps and other work-consuming devices For refrigerators, heat pumps and other work-consuming devices. The second law efficiency is expressed as: In general, the second law efficiency is expressed as:

Example: A dealer advertises that he has just received a shipment of electric resistance heaters for residential buildings that have an efficiency of 100%, as shown in fig. Assuming an indoor temperature of 21OC and outdoor temperature of 10OC, determine the second law efficiency of the heaters

The exergies of a fixed mass (nonflow exergy) and of a flow stream are expressed as:

The exergy change of a fixed mass or fluid stream as it undergoes a process from state 1 to state 2 is given by Nonflow exergy or exergy of fixed mass Flow exergy

Example: A 200m3 rigid tank contains compressed air at 1 MPa and 300K Example: A 200m3 rigid tank contains compressed air at 1 MPa and 300K. Determine how much work can be obtained from this air if the environment conditions are 100 kPa and 300 K. The mass of air in the tank is The exergy content of the compressed air

Therefore, and

Example: Refrigerant 134a is to be compressed from 0 Example: Refrigerant 134a is to be compressed from 0.14 MPa and -10OC to 0.8 MPa and 50OC steadily by a compressor. Taking the environment conditions to be 20OC and 95kPa, determine the exergy change of the refrigerant during this process and the minimum work input that needs to be supplied to the compressor per unit mass of the refrigerant. Inlet State: Exit State:

The exergy change of the refrigerant during this compression process is determined as Therefore, the exergy of the refrigerant will increase during compression by 37.9kJ/kg

Exergy can be transferred by heat, work and mass flow Exergy transfer accompanied by heat, work and mass transfer are given as: Exergy transfer by heat:

Exergy transfer by work: Exergy transfer by mass:

Decrease of Exergy Principle The exergy of an isolated system during a process always decreases or in the limiting cases of a reversible process, remains constant. This is known as the decrease of exergy principle and is expressed as:

Exergy Destruction Irreversibilites always generate entropy, and anything that generates entropy always destroys exergy. The exergy destroyed is proportional to the entropy generated and is expressed as Exergy destroyed is a positive quantity for any actual process and becomes zero for a reversible process. Exergy destroyed represents the lost work potential.

Exergy Balance: Closed Systems The exergy change of a system during a process is equal to the difference between the net exergy transfer through the system boundary and the exergy destroyed within the system boundaries as a result of irreversibilities. General form: Rate form:

Exergy Balance: Control Volume The rate of exergy change within the control volume during a process is equal to the rate of net exergy transfer through the control volume boundary by heat, work and mass flow minus the rate of exergy destruction within the boundaries of the control volume or