Advanced Thermodynamics: Lecture 8 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in August 20, 2015 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy or Availability Work potential of an energy source – is the amount of energy that can be extracted as useful work. This property is exergy, which is also called the availability or available energy. Recall that the work done during a process depends on the initial state, the final state, and the process path. Work = f (initial state, process path, final state) The work output is maximized when the process between two specified states is executed in a reversible manner. Therefore, all the irreversibilities are disregarded in determining the work potential. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy or Availability A system is said to be in the dead state when it is in thermodynamic equilibrium with the environment. At the dead state, a system is at the temperature and pressure of its environment (in thermal and mechanical equilibrium); it has no kinetic or potential energy relative to the environment (zero velocity and zero elevation above a reference level); and it does not react with the environment (chemically inert). Also, there are no unbalanced magnetic, electrical, and surface tension effects between the system and its surroundings, if these are relevant to the situation at hand. The properties of a system at the dead state are denoted by subscript zero, for example, P 0 , T 0 , h 0 , u 0 , and s 0 . Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy or Avalability Distinction should be made between the surroundings, immediate surroundings, and the environment. Surroundings are everything outside the system boundaries. The immediate surroundings refer to the portion of the surroundings that is affected by the process, and environment refers to the region beyond the immediate surroundings whose properties are not affected by the process at any point. A system delivers 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. Exergy represents the upper limit on the amount of work a device can deliver without violating any thermodynamic laws. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy or Avalability Unavailable energy Total energy Exergy Unavailable energy is the portion of energy that cannot be converted to work by even a reversible heat engine. Image: Thermodynamics: An Engineering Approach by Cengel and Boles 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy Transfer from a Furnace Consider a large furnace that can transfer heat at a temperature of 2000 R at a steady rate of 3000 Btu/s. Determine the rate of exergy flow associated with this heat transfer. Assume an environment temperature of 77F. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy (Work Potential) Associated with Kinetic and Potential Energy Exergy of Kinetic Energy x ke = ke = V 2 2 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Exergy (Work Potential) Associated with Kinetic and Potential Energy Exergy of Kinetic Energy x ke = ke = V 2 2 Exergy of Potential Energy x pe = pe = gz Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
The work done by work-producing devices is not always entirely in a usable form. For example, when a gas in a pistoncylinder device expands, part of the work done by the gas is used to push the atmospheric air out of the way of the piston. 428 | Thermodynamics Atmospheric Atmospheric air air P 0 P 0 SYSTEM SYSTEM V 2 V 1 FIGURE 8–8 This work, which cannot be recovered and utilized for any useful purpose, is equal to the atmospheric pressure P 0 times the volume change of the system, The difference between the actual work W and the surroundings work W surr is called the useful work W u W u = W − W surr = W − P 0 ( V 2 − V 1 ) Image: Thermodynamics: An Engineering Approach by Cengel and Boles 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 � �
Reversible work W rev is defined as the maximum amount of useful work that can be produced (or the minimum work that needs to be supplied) as a system undergoes a process between the specified initial and final states. When the final state is the dead state, the reversible work equals exergy. Any difference between the reversible work W rev and the useful work W u is due to the irreversibilities present during the process, and this difference is called irreversibility I. I = W rev , out − W u Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
The Rate of Irreversibility of a Heat Engine 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. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Irreversibility during the Cooling of an Iron Block A 500-kg iron block is initially at 200C and is allowed to cool to 27C by transferring heat to the surrounding air at 27C. Determine the reversible work and the irreversibility for this process. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Heating Potential of a Hot Iron Block The iron block discussed previous example is to be used to maintain a house at 27C when the outdoor temperature is 5C. Determine the maximum amount of heat that can be supplied to the house as the iron cools to 27C. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
�� � � Second Law efficiency Thermal efficiency and the coefficient of performance for devices are defined as a measure of their performance. They are defined on the basis of the first law only, and they are sometimes referred to as the first-law efficiencies. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency Thermal efficiency and the coefficient of performance for devices are defined as a measure of their performance. They are defined on the basis of the first law only, and they are sometimes referred to as the first-law efficiencies. Source Source 1000 K 600 K A B η th = 30% η th = 30% η = 50% η = 70% th,max th,max Sink 300 K Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 �� � �
Second Law efficiency Thermal efficiency and the coefficient of performance for devices are defined as a measure of their performance. They are defined on the basis of the first law only, and they are sometimes referred to as the first-law efficiencies. Source Source 1000 K 600 K A B η th = 30% η th = 30% η = 50% η = 70% th,max th,max Sink 300 K Engine B has greater availability. Image: Thermodynamics: An Engineering Approach by Cengel and Boles 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 �� � �
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev η II = W u (work producing device) W rev Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev η II = W u (work producing device) W rev η II = W rev (work consuming device) W u Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev η II = W u (work producing device) W rev η II = W rev (work consuming device) W u COP η II = (ref and heat pumps) COP rev Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev η II = W u (work producing device) W rev η II = W rev (work consuming device) W u COP η II = (ref and heat pumps) COP rev η II = Exergy supplied Exergy Available = 1 − Exergy destroyed Exergy Available Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law efficiency η II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions η th η II = η th , rev η II = W u (work producing device) W rev η II = W rev (work consuming device) W u COP η II = (ref and heat pumps) COP rev η II = Exergy supplied Exergy Available = 1 − Exergy destroyed Exergy Available Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second-Law Efficiency of Resistance Heaters A dealer advertises that he has just received a shipment of electric resistance heaters for residential buildings that have an efficiency of 100 percent. Assuming an indoor temperature of 21C and outdoor temperature of 10C, determine the second-law efficiency of these heaters. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
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