Air standard and power cycles: Otto, Diesel, Dual and Brayton cycles â their description and representation on .... It can however, exchange energy in the form of work with its surroundings. 1.6 Control ... surrounding which cannot recovered.
Thermodynamics
Mohd Parvez Department of Mechanical Engineering Al-Falah University (India)
Al-Falah University Department of Mechanical Engineering Course Description Course Title: Thermodynamics Course Category: DC Course Code: ME 201 L T P Structure: 3-1-0 Credits: 3
Internal Marks: 60 External Marks: 90 Total Marks: 150 Exam Duration: 2-30 hrs
Course Objectives The subject matter taught in this course will enable the students to: understand the concept of thermodynamic systems, control volume, intensive and extensive properties, work and heat interactions. understand the laws of thermodynamics and their important consequences/corollaries. know about ideal and real gases, pure substance and phase change. analyse the air standard cycles on the basis of efficiency and mean effective pressure. relate thermodynamic properties via partial derivatives, Maxwell relations and T – ds equations.
Course Contents Unit – 1 Basic concepts: Thermodynamics; Thermodynamic system, surrounding and boundary; System and control volume; Thermodynamic properties of a system, state, path, process and cycle; Quasi-static, reversible and irreversible processes; Homogeneous and heterogeneous systems; Working fluids; Thermodynamic equilibrium; Zeroth law of thermodynamics and temperature scales. Energy and its different forms: Energy, forms of energy; Thermodynamic work and heat; Joule‟s experiment and First law of Thermodynamics; First Law for a cycle and change of state – internal energy and enthalpy; pdV work and its evaluation for different thermodynamic processes; First law for closed system (control mass) and open system (control volume); Steady flow energy equations (SFEE) and its engineering applications; Free expansion and throttling processes. 1
Unit – 2 Second law of thermodynamics and its necessity: Limitations of the first law of thermodynamics; Thermal reservoir, source and sink; Kalvin – Planck‟s and Clausius statements of second law of thermodynamics and their equivalence; Refrigerator and heat pump; Carnot cycle; Carnot theorem and corrollaries; Thermodynamic temperature scale Entropy and principle of entropy growth: Definition and physical concept of entropy; Temperature – entropy plot and entropy change during a process; Concept of high and low grade energy, Available and unavailable energy; Law of degradation of energy; Useful work and dead state; Availability and its changes for a non-flow (closed) and steady flow systems; Second law efficiency and elementary treatment of third law of thermodynamics (Nernst Law).
Unit – 3 Concept of ideal and perfect gas: Perfect gas laws; Equation of state and characteristic gas equation; Avogadro‟s law and universal gas constant; Deviation from perfect gas model – vander walls equation of state; Reduced coordinates; Compressibility factor and law of corresponding states. Mixture of perfect gases: Mole fraction and mass fraction; Dalton‟s law of partial pressures; Amagat Leduc law; Equivalent gas constant; Specific heats and entropy of a mixture of perfect gases; Thermodynamic relations: Maxwell‟s equations and T-dS equations; Heat capacity relations for internal energy and enthalpy.
Unit – 4 Pure substances: p-v, p-T and T-s diagrams for a pure substance; Phase transformation: Critical point and triple point; Saturation states; Liquid vapour mixtures; Properties of wet, dry and superheated steam; Use of steam tables; Property changes during steam processes; Throttling process and measurement of dryness fraction. Air standard and power cycles: Otto, Diesel, Dual and Brayton cycles – their description and representation on p-V and T-s diagrams; Comparison of Otto, Diesel and Dual combustion cycles on the basis of thermal efficiency and mean effective pressure.
Text / Reference Books 1. Engineering Thermodynamics (Principles and Practices) D S Kumar S K Kataria and Sons, New Delhi
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2. Engineering Thermodynamics P K Nag Tata McGraw Hills, New Delhi 3. Thermodynamics, an Engineering Approach Cengel Y Al and Boles MA Tata McGraw Hills, New Delhi 4. Fundamentals of Engineering Thermodynamics Sonntag R E, Borgnakke C and Van Wylen G J John Wiley and Sons, New Delhi 5. Fundamentals of Engineering Thermodynamics Michael J Moran Wiley India Pvt. Ltd, New Delhi The question paper will have nine questions in all. Q. No. 1 will be compulsory and will be of conceptual nature covering the entire syllabus. There after there will be four sections and each section will have two questions. Candidates will be required to attempt only one question from each section. All questions carry equal marks and the duration of examination will be 2.30 hrs.
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Unit – 1 Basic Concepts 1.1 Introduction Thermodynamics differentiates two kinds of energy: 1. Organized forms of energy can be completely converted into any other forms of energy such as mechanical, electrical, gravitational etc. 2. Disorganized forms of energy that is thermal energy cannot be fully converted into organized forms of energy due to irreversibilities such as thermal energy or heat. Thermodynamics comes from “therme” (heat) and “dynamis” (power) in Greek word, which is most descriptive of early effort to convert heat into power. The term thermodynamics was first used in publication by Lord Kelvin in 1849. The first thermodynamics textbook was written in 1859 by William Rankine, a professor at the University of Glasgow. Thermodynamics is commonly defined as the science of energy and entropy. Basically, thermodynamics is a science and more importantly, an engineering tool used to describe processes that involve changes in temperature, transformation of energy, and the relationships between heat and work. It is used to describe the performance of propulsion systems, power generation systems and refrigerators, and to describe fluid flow, combustion and many other phenomena. In otherworld‟s we say that, thermodynamics is the science that deals with heat and work and those properties of substances that bear a relation to heat and work. As with all sciences, the basis of thermodynamics is experimental observation and findings. These findings have been formalized into certain basic laws, which are known as first, second and third law of thermodynamics.
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1.1.1 Application areas of thermodynamics Thermodynamics is commonly encountered in many engineering systems and other aspects of life, and one does not need to go very far to see some application areas of it. The heart is constantly pumping blood to all parts of the human body, various energy conversion occurs in trillions of body cells, and the body heat generated is constantly rejected to the environment. We try to control heat transfer rate of our body by adjusting our clothing to the environment condition. Other examples: the electric or gas range, the heating and air – conditioning system, the refrigerator, the pressure cookers, the water heater, the iron and computer. On a large scale, thermodynamics plays a major part in design and analysis of automotive engines, rocket, jet engines and conventional or nuclear power plants, solar collectors etc. 1.1.2 Pioneers of thermodynamics Thermodynamics was formalized as a science in the nineteenth century by the following: Joule (1818-1889) Kelvin (1824-1907) Clausius (1822-1888) Carnot (1792-1832) Gibbs (1839-1903) 1.2 Macroscopic approach The state of matter is described by specifying only a small number of variables, considering average activity of constituent molecules, such as pressure, temperature and velocity. In the macroscopic approach, a certain quantity of matter is considered, without the events occurring at the molecular level being taken into account. Macroscopic thermodynamics is only concerned with the effects of the action of many molecules, and these effects can be perceived by human sense. For example, the macroscopic quantity, pressure, is the average rate of change of momentum due to all the molecular collisions made in a unit area. 5
For example, in the piston – cylinder assembly of an IC engine, the volume occupied by the gas for each position of the piston can be determined by measuring the cylinder diameter and piston travel. The pressure exerted by the gas and its temperature can be measured by means of a pressure gauge and a thermocouple respectively. Attention is focused on a certain quantity of matter without taking into account the events occurring at molecular level Analysis is concerned with gross or overall behavior of the system, and this approach is adopted in the study of classical thermodynamics A few properties are needed to describe the system The properties like pressure and temperature etc needed to describe the system can be easily measured, and felt by our sense The macroscopic approach requires simple mathematical formulae for analyzing the system 1.3 Microscopic approach The state of matter is described by specifying the behaviour of individual molecule such as position, velocity vector and the intermolecular forces that exist among them. Matter constituting the system is considered to comprise a large number of discrete particles called molecules. These molecules have different velocities and energies, and these parameters constantly change with time Adopted in the study of statistical thermodynamics Large number of variables are needed to described the system The properties like velocity, momentum and kinetic energy which describe the behaviour of the molecules can neither be felt our senses nor easily measured by instruments The properties are defined for each molecule individually 1.4 Thermodynamic system The fundamental concept of thermodynamics is the thermodynamic system proposed by Carnot (1824). By definition, a thermodynamic system is defined as a quantity of matter or a region in space upon which attention is concentrated in the analysis of a problem. Everything external to the system is called the surroundings or the environment. The system is separated by the surrounding by the system boundary. The boundary may be either fixed or moving. For the 6
purpose of a thermodynamic analysis, the universe is divided into two parts, the thermodynamic system and surroundings. A system and its surrounding together comprise a thermodynamic system as shown in Figure 1.1. It may be divided into three categories: Boundary
System
Surroundings Figure 1.1 Thermodynamic system 1.4.1 Closed system: There is no mass transfer across the system boundary. There may be energy transfer into or out of the system in the form of heat and work with its environment. The mass within the system remains the same and constant, through its volume can change against a flexible boundary as shown in Figure 1.2. For example: refrigerator, freezer, cooker.
Boundary Energy out System Energy in Surroundings Figure 1.2 Closed system 1.4.2 Open system: An open system is one in which matter flow into or out of the system. In otherworld‟s, open system is one in which matter cross the boundary of the system. There may be energy transfer also in the form of heat and work. The mass within the system does not necessarily remain constant; it may depend upon the mass inflow and mass outflow as shown in 7
Figure 1.3. Examples: Air compressor in which air enters at low pressure and leaves at high pressure, boiler, steam generator. Boundary Energy in Mass out System Mass in Surroundings
Energy out
Figure 1.3 Open system 1.4.3 Isolated system: An isolated is that system which exchange neither energy nor matter with any other system or with environment, means fixed mass as well as energy. An isolated system has no interaction with the surroundings. The universe can be considered as an isolated system as shown in Figure 1.4. Another important example: Thermo flask
System
Surroundings Figure 1.4 Isolated system 1.5 Adiabatic system: There exists wall or boundaries which do not allow heat transfer to take place across them. An adiabatic system is one which is thermally insulated from its surrounding. It can however, exchange energy in the form of work with its surroundings. 1.6 Control volume: Control volume is a properly selected region in space. It usually enclosed a device that involves mass flow such as a compressor, turbine, or nozzle. Flow through these 8
devices is best studied by selecting the region within the device as the control volume as shown in Figure 1.5. A large number of engineering problems involve mass flow in and out of a system and, therefore, are modeled as control volumes.
CV (Nozzle)
Figure 1.5 Control volume 1.7 Thermodynamics properties of system: In engineering problem, for any fluid which is used as working fluid, the six basic thermodynamic properties required are: Pressure, Temperature, Volume, Internal Energy, Enthalpy and Entropy. 1.7.1 System properties: Properties of a system are a characteristic of the system, such as pressure, temperature, and volume. Properties may be of two types: 1.7.1.1 Intensive properties: Intensive properties that do not depend on the mass of the system. For example: pressure and temperature, density and chemical potential. 1.7.1.2 Extensive properties: An extensive property essentially depends on the mass of a system. For example: volume, energy (entropy, enthalpy). If the mass increased, the value of extensive properties also increases. 1.7.2 State: When all the properties of a system have definite values, the system is said to exit at a definite state. 1.7.2.1 Change in state: Any operation in which one or more of the properties of a system change is called a change of state. 1.7.3 Path: The succession of states passed through during a change of state is called the path of change of state. 1.7.4 Process: When the path is completely specified, the change of state is called a process. For example: A constant pressure process.
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When the path is completely specified, the change of state is called a process. In other words, a system undergoes a change in state due to energy and mass interaction with the surroundings. A mode as to how this change occurs is called a process. It may be a Constant pressure (isobaric) process Constant volume (isochoric) process Constant temperature (isothermal) process Constant entropy (isentropic) process 1.7.5 Thermodynamic cycle: A thermodynamic cycle is defined as a series of state changes such that the final state is identical with initial state. 1.8 Quasi – state process Quasi means almost A process which is almost stationary A quasi static process is also called a reversible process Properties of the system are uniform at any instant during a process i.e. state is well defined This is a succession of equilibrium state and portrays infinite slowness in its characteristic features A quasi-static process is also called a reversible process. This is a secession of equilibrium states and portrays infinite slowness in its characteristic features. Example: very slow compression of gas inside the cylinder. 1.9 Reversible process: A reversible process is one which is performed in such a way that at the conclusion of the process, both the system and the surroundings, may be restored to their initial states, without producing any changes in the rest of the universe. This is possible only if the net heat and network exchange between the system and the surrounding is zero for the combined (original and reversible process). 1.9.1 Reversible cycle: If a system undergoes a reversible cycle than after completion of the cycle the system as well as the surrounding will be their original state. If an engine runs on a reversible cycle and produces a work W after receiving heat, it will be able to transfer heat from cold body if work W is supplied to it. No practical cycle can be reversible because heat exchange
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takes place with surrounding which cannot be reversible because heat exchange takes place with surrounding which cannot recovered. 1.9.2 Irreversibility: The actual work done by a system is always less than the idealized reversible work, and the difference between the reversible work and the actual work is called irreversibility of the process. In otherworld‟s, irreversibility can be defined as the difference between the reversible and the actual work obtained from the system during a process. Mathematically,
Hence it can also be defined as the lost of opportunity to do work The above equation is called Gouy – Stodala theorem which state that by calculating the total entropy generation of the system and multiplying it with
(ambient temperature) one can
calculate the irreversibility in the system. The main causes of irreversibility are: Heat transfer due to finite temperature difference Pressure drop or frication Mixing of two fluids Interaction of system with the external masses 1.10 Irreversible process or natural process: An irreversible process does not trace the same path when reversed. The irreversibility may be due to: fraction; heat flow (always from hot to cold); mixing of two fluids (different) in different states. The processes that are not reversible are called irreversible processes. “When a system changes its state very slowly under the influence of very small finite differences of temperature and pressure, it may be assumed that the system is doing so through the attainment of successive stages, which are very close to the equilibrium” 1.11 Phase: A quantity of matter homogeneous throughout in chemical composition and physical structure is called a phase. Every substance can exit in any one of the three phases such as solid, liquid, and gas. 1.11.1 Homogeneous system: A system which consists of a single phase is termed as homogeneous system. For example: mixture of air and water vapor (solid, liquid and gas). 11
1.11.2 Heterogeneous system: A system which consists of two or more phases is called heterogeneous system. For example: water plus steam etc. 1.12 Working fluids: Working fluid refers to the fluid employed in thermodynamic devices to serve as a medium for the transport of energy between the system and surroundings. A working fluid is a fluid inside a closed system that facilitates its function, such as heating, cooling, or electricity generation. Fluids may be gas, vapor, liquid or non-chemically reactive mixture of these constitutes the matter normally considered in engine rings thermodynamics. Fluid can be made to absorb, store and release energy. In other words, a working fluid is a pressurized gas or liquid that actuates a machine. Examples include steam in a steam engine, air in a hot air engine and hydraulic fluid in a hydraulic motor or hydraulic cylinder. More generally, in a thermodynamic system, the working fluid is a liquid or gas that absorbs or transmits energy. Applications and examples Application
Typical working fluid
Gas turbine cycles
Air
Rankine cycles
Water/steam, Chlorofluorocarbons
Vapor compression refrigeration/heat pump
Chlorofluorocarbons, fluorocarbons, ammonia, propane, sulfur dioxide, butane
The steam engine is another example of a system that relies on a working fluid. Heating water turns it to steam, generating pressure and creating energy to make electricity or drive an engine. The engine in this case needs a constant supply of new water, as the steam evaporates as it moves through the engine. It may transport easily from one place to another place through pipes. 1.13 Thermodynamic equilibrium: A system is said to exit in a state of thermodynamic equilibrium when no change in any microscopic properties is registered, if the system is isolated from its surroundings. A system will be in a state of thermodynamic equilibrium, if the conditions for the following three types of equilibrium are satisfied. 1.13.1 Mechanical equilibrium: In the absence of any unbalanced forces within the system itself and also between the system and the surrounding are known as mechanical equilibrium. The pressure in the system is same at all points and does not change with time. 12
1.13.2 Chemical equilibrium: If there is no chemical reaction or transfer of matter from one part of the system to another are known as chemical equilibrium. The chemical composition which is same throughout the system does not vary with time. 1.13.3 Thermal equilibrium: When a system existing in mechanical and chemical equilibrium is separated from its surrounding by a diathermal wall and if there is no change in any properties of system is known as thermal equilibrium. The temperature will be the same at all points of the system does not change with time. When the conditions for any one of three types of equilibrium are not satisfied, a system is said to be in a non-equilibrium state. 1.14 Zeroth law of thermodynamics: The zeroth law of thermodynamics is a statement about thermodynamic equilibrium expressed as follows; if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. A system at internal equilibrium has a uniform pressure, temperature, and chemical potential throughout its volume. It is the basis of temperature measurement. 1.15 Temperature scale: There are three temperature scales in use today, Fahrenheit, Celsius and Kelvin. Fahrenheit temperature scale is a scale based on 32 for the freezing point of water and 212 for the boiling point of water, the interval between the two being divided into 180 parts. Celsius temperature scale also called centigrade temperature scale, is the scale based on 0 for the freezing point of water and 100 for the boiling point of water. Invented in 1742 by the Swedish astronomer Anders Celsius, it is sometimes called the centigrade scale because of the 100-degree interval between the defined points. The following formula can be used to convert a temperature from its representation on the Fahrenheit (F) scale to the Celsius (C) value: C = 5/9(F - 32). Kelvin temperature scale is the base unit of thermodynamic temperature measurement in the International System of measurement. It is defined as 1/ 273.16 of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water. Such a scale has as its zero point absolute zero, the theoretical temperature at which the molecules of a substance have the lowest energy. The Kelvin scale is related to the Celsius scale. The difference between the freezing and boiling points of water is 100 degrees in each, so that the kelvin has the same magnitude as the degree Celsius.
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1.16 Force: The force acting on a body is defined by Newton‟s second law of motion. 1 N= 1kg m/s2 1.17 Pressure: Pressure is the normal force exerted by a system against unit area of the boundary surface. I bar=105 pa =100 kpa =0.1 Mpa In thermodynamics, some of the following pressure terms are frequently used in connection with energy transfers. 1.17.1 Atmospheric pressure: It is the pressure exerted by air on the surface of the earth. Since earth being round in shape, its level is different at different places and hence pressure exerted by air also varies from place to place. The numerical value of pressure at mean sea level is 1.01325 bar or 760 mm height of mercury column. It is also equivalent to 10.336 meter of water column and 101325 pascal. 1.17.2 Gauge pressure: The pressure relative to the atmosphere is called gauge pressure. This pressure is recorded by gauge, which is a pressure measuring device. This device measure zero pressure under the influence of a fluid and pressure of the atmosphere. 1.17.3 Absolute pressure: Total pressure exerted by a fluid on the walls of a container is called absolute pressure. It is important to note that the absolute zero pressure will occur only when there is perfect vacuum. So, therefore, the pressure relative to a perfect vacuum is called absolute pressure. Absolute pressure= gauge pressure+ atmospheric pressure 1 atm = 101.325 kpa = 1.01325 bar 1.17.4 Vacuum pressure: If the pressure exerted by a fluid on the walls of the container is less than the pressure exerted by the atmosphere the pressure gauge reads a negative pressure. This negative pressure is called vacuum pressure. Absolute pressure= Atmospheric pressure – vacuum pressure 1.18 Temperature: A temperature is the indicator of hotness of a body. In thermodynamic sense the temperature determines in which direction the heat will flow. The heat flows from higher to lower temperature. Zero Kelvin is equal to -2730C or K= 0C+273 Kelvin scale is also known as absolute temperature.
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Energy and Its Different Forms 1.19 Energy: Energy is the capacity to exert a force through a distance, and manifests itself in various forms.
Engineering processes involve the conversion of energy from one form to
another. Unit of energy J (Joule) The energy per unit mass is the specific energy in J/kg 1.19.1 Power: The rate of energy transfer or storage is called power. 1 W= I J/s= 1 Nm/s 1 kW=1000 W 1.20 Forms of energy: There are different forms of energy which are explained below: 1.20.1 High grade energy: High grade energy is the energy that can be completely transformed into mechanical work (shaft work) without any loss. Examples are: Mechanical work Tidal energy Electrical work Kinetic energy of jets Tidal energy Animal and manual energy Wind energy. 1.20.2 Low grade energy: Low grade energy is the energy that cannot be completely converted into mechanical work. For example: Thermal energy Nuclear energy Heat available from combustion of fuel, such as coal and wood. 1.20.3 Available energy: Complete conversion of low grade energy into a high energy is not possible. That parts of the low grade energy which is available for conversion into work is called available energy or energy, and the rest is unattainable energy, called unavailable energy or energy. It was Maxwell (1871) who first coined the term available energy however he credited kelvin with the original ideas.
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1.21 Work: Work is one of the basic modes of energy transfer. In mechanics the action of force on a moving body is identified as work. In thermodynamics, work transfer is considered as occurring between the system and surroundings. 1.22 Heat: Heat is the energy transferred due to temperature difference only. Heat transfer can alter system state Body, s don‟t “contained” heat, heat is identified as it comes across system boundaries. The amount of heat needed to go from one state to another is path dependent. Heat is defined as the form of energy that is transferred across the boundary by virtue of a temperature difference which is denoted by symbol Q. The direction of heat transfer is taken from the high temperature system to the low temperature system. Heat flow into the system is taken to be positive and heat flow out of a system is taken as negative. 1.23 Joule’s experiment: It was well known that heat and work both change the energy of a system. Joule conducted a series of experiments which showed the relationship between heat and work in a thermodynamic cycle for a system. He used a paddle to stir an insulated vessel filled with fluid. Let us consider a closed system which consists of a mass of water contained in an adiabatic vessel having thermometer and a paddle wheel as shown in Figure.
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Let a certain amount of work W1-2 be done upon the system by paddle wheel. The quantity of work can be measured by the fall of weight which derives the paddle wheel through a pulley. The system was initially at temperature T1, the same as that of atmosphere and after work transfer let the temperature rise to T2. The pressure is always 1 atmospheric. The process 1-2 undergo by the system as shown in above Figure. Let the insulation now removed, the system and surrounding interact by heat transfer till the systems returns to the original temperature T1, attaining the condition of thermal equilibrium with the atmosphere. The amount of heat transfer Q2-1 from the system during this process can be estimated. The system has executes the cycle, which consist of a definite amount of work input W1-2 to the system followed by the transfer amount of heat Q2-1 from the system. It has been found that this W1-2 is always proportional to the heat Q2-1 and the constant of proportionality is called Joule‟s equivalent or mechanical equivalent of heat. Mathematically
Where
denotes the cyclic integral for closed path
Note: Adiabatic means thermally insulated from its surrounding, however exchange work with surrounding. 1.24 First law of thermodynamics: In the preceding lectures, we applied the first law of thermodynamics, or the conservation of energy principle, to processes involving closed systems. Energy is a conserved property, and no process is known to have taken place in violation of the first law of thermodynamics. Therefore, it is reasonable to conclude that a process must satisfy the first law to occur. However, as explained below, satisfying the first law alone does not ensure that the process will actually take place. First law of thermodynamics deals with the fact of energy conservation, which means if system looses energy in one form it must gain energy in another form at the same point, so that total quantity of energy remains constant. The law of conservation which state that, although energy can change form, it can be neither created nor destroyed. However, it provides no information about the direction in which processes can occurs, i.e. the reversibility aspects of thermodynamic processes. The first law of thermodynamics provides no information about the inability of a 18
thermodynamic process to convert heat fully into mechanical work. Deals with quantity and governs with law of conservation. Analysis simply provides the overall performance of the system Makes no distinguish between the quality and quantity Provides no information about the direction in which process can occurs Provides no information about thermodynamic process to convert heat fully into mechanical work First law owes to J P Jules, during the period 1840-1849, carried out a series of experiments to investigate the equivalence of work and heat Provides the sound bases for studying the relationships amongst the various forms of energy and energy interaction Based on experimental observation It is common experience that a cup of hot coffee left in a cooler room eventually cools off.
This process satisfies the first law of thermodynamics since the amount of energy lost by the coffee is equal to the amount gained by the surrounding air. Now let us consider the reverse process-the hot coffee getting even hotter in a cooler room as a result of heat transfer from the room air. We all know that this process never takes place. Yet, doing so would not violate the first law as long as the amount of energy lost by the air is equal to the amount gained by the coffee. It is clear from the above that processes proceed in a certain direction and not in reverse direction. The first law places no restriction on the direction of a process, but satisfying the first law does not ensure that that process will occurs in which direction. Another example: A rock at some elevation processes some potential energy and part of this potential energy is converted into kinetic energy as the rock falls. Experimental data shows that,
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the decrease in potential energy exactly equal to increase in kinetic energy when air resistance is negligible. 1.24.1 First law for a cycle: Since the initial and final states are identical in a thermodynamic cycle, the system experiences no net change in state. Therefore, the system also experiences no net change in energy for the cycle.
0
or In words, the first law of thermodynamics or the conservation of energy principle applied to a cycle: [Net energy transferred by heat for the cycle] = [Net energy transferred by work for the cycle] 1.24.2 First law of thermodynamics for an open system: A thermodynamic system becomes an open system, if there is an exchange of mass between the system and its surroundings in addition to the work and heat transfer interaction. To study such systems, a concept of control volume is required which is simply a finite region in space through which mass, momentum and energy can transfer. The boundary of control volume is known as control surface. A control volume shown below can be analyzed as an open system.
Qc v
Fluid flow out Fluid flow in
Control volume Wcv
Open System
Control surface
The general first law equation for thermodynamic process is
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For application of the open system, the energy term „E‟ will include internal energy, gravitational, potential energy and kinetic energy. 1.24.3 First law for closed system: For any closed system taken through a cyclic process, the network delivered to surroundings is equal to the net heat taken from surroundings That is δQ = δW E = U+ K.E + P.E E = Total energy
(kJ)
U = Total internal energy
(kJ)
H = Total enthalpy
(kJ)
K.E = Total kinetic energy
(kJ)
P.E= Total kinetic energy
(kJ)
Mathematically Q–W=
(For general system)
Q–W=
(For open system)
Q– W =
(For closed system)
Q1-2 – W1-2 = E2 – E1 (Ist law for a process) Q1-2 – W1-2 = For unit mass of the system can be written as q1-2– w1-2 = q1-2– w1-2 =
(For closed system)
1.25 Study flow energy equation (SFEE): Fluid enters the control volume at section1 with velocity V1, pressure p1, specific volume v1, internal energy u1 and mass m1. Corresponding values at the exit section 2 are V 2, p2, v2, u2, m2. Further during the fluid flow between the two sections, heat q and mechanical work W may also cross the boundary of the control surface. Energy between equation
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We know that
The study flow energy equation can be written on the basis of unit mass
Control surface
1 Steady Flow Plant
W
Z1 Arbitrary datum line
2
Q Z2
1.26 Engineering applications study flow energy equation: The application of steady flow energy equation can be used to study the performance of many engineering devices that undergo thermodynamic processes, as these devices closely satisfy the conditions for steady flow processes. For example: The engineering devices like boiler, turbine, condenser/heat exchanger, feed water pump, cooling tower and stack of steam power plants run nonstop for many months before these are shut for maintenance. Therefore these engineering devices must run under steady state conditions and can be analyzed as steady flow devices by applying steady flow energy equation. 1.27 Free expansion: Free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. It is also called Joule expansion. Real gases experience a 22
temperature change during free expansion. For an ideal gas, the temperature doesn't change, and the conditions before and after adiabatic free expansion satisfy. Consider two vessels 1 and 2 interconnected by a short pipe with a valve A and perfectly thermally insulated. Initially let the vessel 1 filled with a fluid at certain pressure and let 2 be completely evacuated (vacuum). When the value A is opened the fluid in 1 will expand rapidly to fill both vessels 1 and 2. The pressure finally will be lower than the initial pressure in vessel 1. This is known as free expansion. This process is highly irreversible. Now applying First law of thermodynamics
In this process no work is done ⸫W=0 The system is isolated, so no heat is transferred ⸫ Q=0 The process is therefore, Adiabatic but irreversible
{In a free expansion the internal energy initially equals the initial energy finally}
⸫ For a perfect gas undergoing a free expansion, the initial temperature is equal to the final temperature. 1.28 Throttling processes: Throttling is the expansion of fluid from high pressure to low pressure. This process occurs when fluid passes through an obstruction (partially opened valve or small orifice) placed in the fluid flow passage. Throttling process is used for finding the dryness fraction of wet steam. From SFEE
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Changes of P.E are very small and ignored. Thus the SFEE reduces to
Pipe velocity in throttling is very low. So the K.E is also negligible
Enthalpy of the fluid before throttling is equal to the entropy of fluid after throttling. Throttling is the expansion of fluid from high pressure to low pressure. This process occurs when fluid passes through an abstraction ( partially opened value or a small orifice) The enthalpy of the fluid before throttling is equal to the enthalpy of the fluid after throttling The pressure drop is realized without a work or heat interaction. W=0
Q=0
No change in P.E. The purpose of throttling process involves change in the phase of the fluid. Used: Used for finding the dryness fraction of wet steam The flow through the expansion valve of a vapour compression refrigeration system.
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