ENGINEERING THERMODYNAMICS MODULE-I LECTURE-1 · the Rankine cycle efficiency, The reheat cycle,...

Prepared by Prof. (Dr.) Manmatha K. Roul

ENGINEERING THERMODYNAMICS

MODULE-I

LECTURE-1

Prepared By

Prof. (Dr.) Manmatha K. Roul Professor and Principal

Gandhi Institute for Technological Advancement (GITA), Bhubaneswar – 752054

June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul ENGINEERING THERMODYNAMICS (PME3I103)

SYLLABUS Theory L/T (Hours per week): 3/0, Credit: 3

Module-I (10 Lectures)

1. Review of First and Second laws:

First law analysis of unsteady flow control volumes, Entropy

generation,Entropybalance for closed systems and steady flow systems, Available

energy, Quality ofenergy, Availability for non flow and flow process,

Irreversibility, Exergybalance, Second law efficiency.

Module- II (12 Lectures)

2. Vapour Power Cycles:

The Carnot vapor cycle and its limitations, The Rankine cycle, Means ofincreasing

the Rankine cycle efficiency, The reheat cycle, The regenerative feedheating cycle,

Cogeneration (Back pressure and Pass-out turbines), Combinedcycle

power generation systems, Binary vapour cycles.

3. Gas Power Cycles:

Air standard cycles- Otto, Diesel, Dual Combustion and Brayton cycles,

TheBrayton cycle with non-isentropic flow in compressors and turbines,

TheBrayton cycle with regeneration, reheating and intercooling, Ideal jet

propulsioncycles.

Module- III (12 Lectures)

Prepared by Prof. (Dr.) Manmatha K. Roul 4. Refrigeration cycles:

Reversed Carnot cycle, Reversed Brayton cycle (Gas refrigeration system),

Thevapor compression cycle, The vapor absorption cycle.

5. General Thermodynamic property relations:

The Maxwell relations, The Clapeyron equation, The TdS relations,

Isothermalcompressibility and volume expansivity, The Joule-Thomson

coefficient.

Module- IV (06 Lectures)

6. Reciprocating Air Compressors:

Introduction (Uses of compressed air), The reciprocating cycle neglecting

andconsidering clearance volume, Volumetric efficiency and its effect on

compressorperformance, Limitations of single stage compression, Multistage

compressionand intercooling, Optimum intercooler pressure, Performance and

designcalculations of reciprocating compressors, Air motors.

Text Books

1. Engineering Thermodynamics by P. K. Nag, Publisher:TMH

2. Engineering Thermodynamics by P. Chattopadhyay, OXFORD

3. Fundamentals of Thermodynamics by Sonntag, Borgnakke, Van Wylen,

JohnWiley & Sons

4. Fundamentals of Engineering Thermodynamics by E. Rathakrishnan, PHI

Prepared by Prof. (Dr.) Manmatha K. Roul

MODULE-I

LECTURE-1

REVIEWS OF LAWS OF THERMODYNAMICS

Thermodynamics is that branch of engineering science which deals with energy transfer andits effect on the physical properties of the substances. The alternate definition of thermodynamics is, it is the science thatdeals with work and heat and those properties of substances that bear a relation to heatand work. Like all sciences, the basis of thermodynamics is experimental observation. Thermodynamics (from the Greek therme, meaning "heat" and dynamis,meaning "power") is a branch of physics that studies the effects of changes intemperature, pressure, and volume on physical systems at the macroscopic scale byanalyzing the collective motion of their particles using statistics. This subject wasdeveloped mainly by the scientists named 1) Carnot 2) Mayer 3) Clausius 4) Joule5) Kelvin 6) Maxwell 7) Plankand 8) Gibbs. In thermodynamics 2 (two) types of energy are considered. One is heat and the other is work. Both of these energies may interact at the boundary of the system. When work energy interacts at the boundary and converts to work only, we need not pay attention to its quality as final form of energy is work only. Heat to work interactions always involves degradation. Work converted to heat is not useful; we call it as dissipation of energy. In thermodynamics basic interest is conversion of heat into work.

Laws of Thermodynamics

The principles of thermodynamics are summarized in the form of four thermodynamic laws.

Prepared by Prof. (Dr.) Manmatha K. Roul The Zeroth Law deals with thermal equilibrium and provides a means for measuring temperatures.

The First Law deals with the conservation of energy and introduces the concept of internal energy.

The Second Law of thermodynamics provides with the guidelines on the conversion of internal energy of matter into work. It also introduces the concept of entropy.

The Third Law of thermodynamics defines the absolute zero of entropy. The entropy of a pure crystalline substance at absolute zero temperature is zero. Apart from these laws, there is another law applied to irreversible thermodynamics developed by Onsagar in the year 1957. This law is termed as fourth law of thermodynamics.

Table given below presents the laws of thermodynamics along with the scientists associated with their invention and year of invention.

Thermodynamic Laws Scientists/Researchers Year

Zeroth Law Fowler and Guggenheim 1939

First Law Joule, Mayer, Thompson and Colding

1845

Second Law Carnot 1824

Third Law Nernst 1907

Fourth Law Onsagar 1968

Different Thermodynamic Laws

Prepared by Prof. (Dr.) Manmatha K. Roul The zeroth law and third law are more definitional in nature. The first and the second laws are more pragmatic and as an engineer we use both these laws for analysis.

Zeroth law gives the definition of temperature.

This law was framed by Ralph Fowler and Guggenheim. Fowler was a British Physicist and astronomer. He named zeroth law of thermodynamics in 1920. Fifteen Fellows of the Royal Society and three Nobel Laureates were supervised by Fowler between 1922 and 1939. He worked with Sir Arthur Eddington, Subrahmanyan Chandrasekhar, Paul Dirac, Sir William McCrea and Milne. Fowler introduced Paul Dirac to quantum theory in 1923. He supervised the doctoral studies of 64 students at Cambridge University, including John Lennard-Jones, Paul Dirac and Garrett Birkhoff.

Edward Armand Guggenheim (1901–1970) was an English thermodynamicist and professor of chemistry at the University of Reading in the year 1939, Guggenheim co-authored a volume entitled Statistical Thermodynamics with Ralph Fowler. The text book by Fowler and Guggenheim on Statistical Thermodynamics was published by Cambridge University Press in 1960.

Temperature is the only property which differentiates thermodymanics from other sciences. The first law is nothing but conservation of energy. Second law indicates the probability of happening of a cycle or process and indicates the direction of energy flow. Further, second law distinguishes the quality of energy. The third law gives the interpretation of a system while marching towards absolute zero temperature.

About the first law of thermodynamics

Simple and most direct statement of the first law of thermodynamics is that energy is conserved. Energy can neither be created nor destroyed. For a cyclic process involving heat and work First Law of Thermodynamics is given

Prepared by Prof. (Dr.) Manmatha K. Roul For a thermodynamic process with heat and work interaction the expression is given by

where E, Q, and W are the energy stored in the system, heat and work interacting at the system boundary, respectively.

• First Law gives a quantative measure of energy • It can not distinguish the different types of energy • It fails to indicate the direction of flow of energy • It can not indicate whether the process is cyclic or not. • First law applied to a process gives rise to a property (internal energy, U for a

closed system and enthalpy, h for a open system)

From the definition of first law, it is obvious that energy is always conserved.

About the second law of thermodynamics

Second law of thermodynamics provides the criterion as to the probability of various processes. Sadi Carnot established this law in 1824. But it got importance from last two decades (1980 onwards) in view of conservation of energy. First law dictates that energy in a system is always conserved. There is no way to conserve energy by use of first law of thermodynamics. However, it is the exergy, which is a consequence of the second law that is never conserved. Unlike energy, exergy always decreases. So minimization of exergy loss is nothing but the principle of energy conservation. The net exergy output to the actual exergy input to the system is the second law efficiency.

whereA = exergy

To improve a system, we always try to improve the second law efficiency. Exergy is a tool to identify the loss of energy. In complicated systems, exergy loss at different locations can give an estimation of such losses and measures can be taken up to reduce the same. Exergy analysis will be discussed in lectures 7-12 of Module 1.

Prepared by Prof. (Dr.) Manmatha K. Roul Apart from the energy conservation, two important implications of second law of thermodynamics are:

Directional flow of energy

A spontaneous process occurs only in one direction. Heat always flows from a body at high temperature to a body at lower temperature, water always flows downhill, time always flows in forward direction. Reverse of these processes never happen spontaneously. The spontaneous process is due to a finite driving potential called FORCE or CAUSE. The outcome or result is called the FLUX, CURRENT or EFFECT.

Table: Forces and fluxes

Sl No Force (Cause) Conjugate fluxes (Effect)

1 Temperature Gradient Heat Transfer

2 Concentration Gradient Mass Transfer

3 Electric Potential Gradient

Flow of Electric Current

TRANSFER PROCESSES CAN NEVER SPONTANEOUSLY OCCUR FROM A LOWER TO A HIGHER POTENTIAL. SECOND

LAW OF THERMODYNAMICS PUTS LIMITATION ON DIRECTION OF PROCESS OCCURANCE.

Qualitative measurement of energy

The second law distinguishes energy in two different forms (1) High grade energy and (2) Low grade energy. High grade energy is an orderly form of energy whereas

Prepared by Prof. (Dr.) Manmatha K. Roul low grade energy is in random form. Some high and low grade energy forms are given in Table 1.6.

Table: Different form of energy

High Grade Energy Low Grade Energy

Electrical energy Thermal Energy from Fossil Fuel

Wind energy Nuclear Fission

Hydropower Nuclear Fusion

Kinetic energy of a water jet

Waste Heat from Thermal Power Plant

Mechanical work Solar Thermal Energy

Tidal power Geothermal Energy

Quality of energy can be ascertained by applying the second law of thermodynamics to a process or a system.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 1


MODULE-I

LECTURE-2

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Thermodynamic Analysis of Control Volumes

A large number of engineering problems involve mass flow in and out of a system and, therefore, are modeled as control volumes (e.g. water heater, radiator, turbine, compressor, etc.) In general, any arbitrary region may be selected as a control volume, but making a proper choice simplifies the solution process.

The boundaries of a control volume are called the control surface, and they can be real or imaginary (e.g. see nozzle below).

A control volume can be fixed in size and shape or possess moving boundaries (e.g. shock absorber).

Few Definitions: steady: implies no change with time; the opposite of transient uniform: implies no change with location

Conservation of Mass Principle: The conservation of mass is one of the fundamental principles in nature. Simply stated it asserts that mass is a conserved property and can not be created or destroyed. The conservation of mass principle for a control volume (CV) undergoing a process can be expressed as:

Where the subscripts i, e, and CV stand for inlet, exit, and control volume, respectively. The conservation of mass equation may also be expressed on a time

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 rate basis by expressing all quantities per unit time .The conservation of mass principle is also often referred to the continuity equation in fluid mechanics.

Mass and Volume Flow Rates:

The amount of mass flowing through a cross-section per unit time is called the mass flow rate and is denoted by. In most practical applications, the mass flow rate in a pipe or duct can be m .

The volume flow rate is the volume of fluid flowing through a cross section per unit time and is given

by:�� = Vav A

Thus, the mass flow and volume flow rates are related by: =

Conservation of Energy Principle:

The first law of thermodynamics attributes the changes in total energy of a closed system to heat and work interactions. For control volumes, however, an additional mechanism can change the energy of a system: mass flow in and out of the control volume! When mass enters a control volume, the energy of the control volume increases because the entering mass carries energy with it. Likewise, when some mass leaves the control volume, the energy contained within the control volume decreases because the leaving mass takes out some energy with it. Then the conservation of energy equation for a control volume undergoing a process can be expressed as

If no mass enters or leaves the control volume, the second and third term above equation becomes the first law for closed systems.

Flow Work: Unlike closed systems, control volumes involve mass flow across their boundaries; work is required to push the mass into or out of the control volume. This is known as flow energy or flow work. The work done in pushing the fluid across the boundary (i.e. flow work) is:


Total Energy of a Flowing Fluid:

The total energy of closed system (non-flowing fluid) is expressed as:

The fluid entering or leaving a control volume possesses an additional form of energy--the flow energy Pv. Then the total energy of a flowing fluid on a unit-mass basis becomes:

But the combination Pv+u has been previously defined as the enthalpy h. So the above relation reduces to:

Steady-Flow Process:

Processes involving steady-flow devices (turbines, compressors, nozzles, etc...) can be represented reasonably well by a somewhat idealized process, called the steady-flow process. A Steady-flow process can be defined as a process during which a fluid flows through a control volume steadily. That is, the fluid properties can change from point to point within the control volume, but at any fixed point they remain the same during the entire process. A steady-flow process is characterized by the following:

No properties (intensive or extensive) within the control volume change with time. As a result, boundary work is zero for steady-flow systems. No properties change at the boundaries (control surface) of the control volume with time. The heat and work interactions between a steady-flow system and its surroundings do not change with time.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 5 Unsteady flow process:

In a steady flow process we have assumed that the mass and energy within the system remain constant and do not vary with time. In an unsteady flow process, mass and energy within the control volume vary continuously. The fluid flow into and out of the system. Example: Filling or evacuation of a tank, (internal energy as well as mass of the tank changes with time), the condition of water in the cylinder jacket of an I.C. engine (is time dependant)

Analysis: Consider the flow of a fluid through a pipe line into the cylinder. Let m1 be the mass of the fluid initially in the cylinder at pressure p1, temperature t1 and m2 the final mass in the cylinder at pressure p2, temperature t2. The mass that flows into the cylinder is thus (m2 – m1).

There are two ways for solving problems involving unsteady flow

(i) Closed system analysis (ii) Control volume analysis

Closed system analysis:

Since no mass crosses the boundary of the system, the boundary of the system is selectedin such a way that it includes not only the cylinder but also that portion of the fluid in thepipe line which will be introduced eventually into the cylinder as shown in figure. Thatmeans the system has variable boundaries which at the final state will be the same as thatof the cylinder. Initially energy of the system E1 is composed of the internal energy of themass initially in the cylinder, m1u1 plus the energy of the fluid which will eventually flowthe pipe line into the cylinder, Since no mass crosses the boundary of the system, the boundary of the system is selected in such a way that it includes not only the cylinder but also that portion of the fluid in the pipe line which will be introduced eventually into the cylinder as shown in figure. That means the system has variable boundaries which at the final state will be the same as that of the cylinder.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 6 Initially energy of the system E1 is composed of the internal energy of the mass initially in the cylinder, m1u1 plus the energy of the fluid which will eventually flow the pipe line into the cylinder,

where the subscript ‘p’ refers to the condition of the fluid in the pipe line. At the final state, energy E2 of the fluid in the system will be equal to m2u2.

Neglecting the change in PE, the change in energy is,

To find out work done on the system, consider a mass in the pipe line (m2 – m1) which is subjected to a controlled pressure Pp. The flow work due to the flow of mass (m2 – m1) into the cylinder from the (m2 – m1) vp in the pipe line to a zero volume is

Prepared by Prof. (Dr.) Manmatha K. Roul Page 7 Where vp is the specific volume of the fluid in the pipeline.

Applying 1st law of thermodynamics,

But

Above equation becomes

Control volume analysis

Prepared by Prof. (Dr.) Manmatha K. Roul Page 8 The cylinder itself is taken as the control volume as shown in figure. In this case, there is no work interaction. Using the general equation 1st law and considering no mass flows out of the control volume and neglecting the change in PE, as in the earlier case we have

If the tank would have been thermally insulated and initially empty, Q = 0 and m1 = 0

Substituting into equation (1) and simplifying, we get

Also if KE in the pipe line is not appreciable, hp = u2 i.e., the specific enthalpy of the fluid in the pipe line is equal to the specific internal energy of the fluid in the cylinder at the final state.

Note: The tank emptying process is the reverse of filling process i.e., there is flow of fluid from the tank (cylinder) to the surroundings. Analogous to filling process, applying 1st law, of thermodynamics, we have

Where hp and Vp are the specific enthalpy and velocity of leaving fluid.

For no heat transfer and negligible exit velocity,

(m1 – m2) hp = m1u1 – m2u2

Further if the tank is to be fully emptied (m2 = 0)

Prepared by Prof. (Dr.) Manmatha K. Roul Page 9 i.e., m1hp = m1u1

or hp = u1

i.e., the specific enthalpy of the fluid in the cylinder is equal to the specific internal energy of the fluid in the pipe line at the final state.

Problems:

1. A household gas cylinder initially evacuated is filled by 15 kg gas supply of

enthalpy 625kJ/kg. After filling, the gas in the cylinder has the following

parameters: pressure 10 bar, enthalpy 750 kJ/kg and specific volume 0.0487

m3/kg. Evaluate the heat received by the cylinder from the surroundings.

2. An insulated and rigid tank contains 5 m3 of air at 10 bar and 425 K. The

air is then let off to atmosphere through a valve. Determine the work

obtainable by utilizing the KE of the discharge air. Take Cp = 1 kJ/kg K, CV

= 0.714 kJ/kg0-K atmosphere pressure = 1 bar.



MODULE-I

LECTURE-3

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Entropy Generation:- The first law of thermodynamics deals with the property energy and the conservation of energy. The second law introduced in the previous chapter, leads to the definition of a new property called entropy. Entropy is defined in terms of a calculus operation, and no direct physical picture of it can be given. In this chapter, Clausius inequality, which forms the basis for the definition of entropy will be discussed first. It will be followed by the discussion of entropy changes that take place during various processes for different working fluids. Finally, the reversible steady-flow work and the isentropic efficiencies of various engineering devices such as turbine and compressors will be discussed. The Clausius Inequality Consider two heat engines operating between two reservoirs kept at temperature TH and TL as shown in the Figure 5.1. Of the two heat engines, one is reversible and the other is irreversible. For the reversible heat engine it has already been proved that 00=

=−

=

∫rev

L

L

H

H

L

H

L

H

TdQ

TQ

TQ

TT

QQ

Prepared by Prof. (Dr.) Manmatha K. Roul As discussed earlier, the work output from the irreversible engine should be less than that of the reversible engine for the same heat input Qwill be greater than QL,Rev . Let us define QL,Irrev = QL,Revthen 00<

−=

−=

−=

∫

L

H

H

L

H

H

Irrev

TdQ

QTQ

TQ

TQ

TdQBy combining this result with that of a reversible engine we get

∫This is known as Clausius inequality

Entropy The Clausius inequality forms the basis for the definition of a new property called entropy.As can be seen in the equation above, for an internally reversible process the cyclicintegral of δQ / T is zero. A quantity whose cyclic integral is zero depends on the state onlyand not the process path, and thus it is a Clausius in 1865 realized that he discovered a new property and he called it entropy: by Prof. (Dr.) Manmatha K. Roul As discussed earlier, the work output from the irreversible engine should be less than that of the reversible engine for the same heat input QH. Therefore Q. Let us define L,Rev + dQ ,,

−LL

revL

L

IrevL

dQTdQ

TQT By combining this result with that of a reversible engine we get 0≤

IrrevTdQ

Clausius inequality. The Clausius inequality forms the basis for the definition of a new property called entropy.As can be seen in the equation above, for an internally reversible process the cyclicintegral of δQ / T is zero. A quantity whose cyclic integral is zero onlyand not the process path, and thus it is a Clausius in 1865 realized that he discovered a new property and he called it Page 3 As discussed earlier, the work output from the irreversible engine should be . Therefore QL,Irrev . The Clausius inequality forms the basis for the definition of a new property called entropy.As can be seen in the equation above, for an internally reversible process the cyclicintegral of δQ / T is zero. A quantity whose cyclic integral is zero onlyand not the process path, and thus it is a property. Clausius in 1865 realized that he discovered a new property and he called it

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 Entropy per unit mass is designated by s (kJ/kg.K). The entropy change of a system during a process can be calculated: To perform this integral, one needs to know the relation between Q and T during the process. Note that the cyclic integral of δQ / T will give us the entropy change only if the integration carried out along an internally reversible path between two states. For irreversible processes, we may imagine a reversible process between the two states (initial and final) and calculate the entropy change (since entropy is a property). The Increase of Entropy Principle Entropy change of a closed system during an irreversible process is greater that the integral of δQ / T evaluated for the process. In the limiting case of a reversible process, they become equal. The entropy generated during a process is called entropy generation, and is denoted by Sgen, Note that the entropy generation Sgen is always a positive quantity or zero (reversible process). Its value depends on the process, thus it is not a property of a system. The entropy of an isolated system during a process always increases, or in the limiting case of a reversible process remains constant (it never decreases). This

Prepared by Prof. (Dr.) Manmatha K. Roul Page 5 is known as the increase of entropy principle. The entropy change of a system or its surroundings can be negative; but entropy generation cannot. 1‐A process must proceeds in the direction that complies with the increase of entropy principle, Sgen> 0. A process that violates this principle is impossible. 2‐ Entropy is a non‐conserved property, and there is no such thing as the conservation of entropy. Therefore, the entropy of universe is continuously increasing. 3‐The performance of engineering systems is degraded by the presence of irreversibility. The entropy generation is a measure of the magnitudes of the irreversibility present during the process.



MODULE-I

LECTURE-4

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June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Entropy Balance:- Entropy is a measure of molecular disorder or randomness of a system, and the second law states that entropy can be created but it cannot be destroyed. The increase of entropy principle is expressed as Entropy change = Entropy transfer + Entropy generation This is called the entropy balance. Entropy Change The entropy balance is easier to apply that energy balance, since unlike energy (which has many forms such as heat and work) entropy has only one form. The entropy change for a system during a process is: Entropy change = Entropy at final state ‐ Entropy at initial state Therefore, the entropy change of a system is zero if the state of the system does not change during the process. For example entropy change of steady flow devices such as nozzles, compressors, turbines, pumps, and heat exchangers is zero during steady operation. Mechanisms of Entropy Transfer Entropy can be transferred to or from a system in two forms: heat transfer and mass flow.Thus, the entropy transfer for an adiabatic closed system is zero. Heat Transfer: heat is a form of disorganized energy and some disorganization (entropy)will flow with heat. Heat rejection is the only way that the entropy of a fixed mass can bedecreased. The ratio of the heat transfer Q/ T (absolute temperature) at a location iscalled entropy flow or entropy transfer

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 Since T (in Kelvin) is always positive, the direction of entropy transfer is the same of the direction of heat transfer. When two systems are in contact, the entropy transfer from warmer system is equal to the entropy transfer to the colder system since the boundary has no thickness and occupies no volume. Note that work is entropy‐free, and no entropy is transferred with work. Mass Flow: mass contains entropy as well as energy, both entropy and energy contents ofa system are proportional to the mass. When a mass in the amount of m enters or leavesa system, entropy in the amount of ms (s is the specific entropy) accompanies it. Entropy Balance for a Closed System A closed system includes no mass flow across its boundaries, and the entropy change is simply the difference between the initial and final entropies of the system. The entropy change of a closed system is due to the entropy transfer accompanying heat transfer and the entropy generation within the system boundaries: Entropy change of the system = Entropy transfer with heat + Entropy generation Therefore, for an adiabatic closed system, we have: For an internally reversible adiabatic process ∆S = 0, because Sgen= 0. The total entropy generated during a process can be determined by applying the entropy balance to an extended system that includes both the system and its immediate surroundings where external irreversibility might be occurring. Entropy Balance for a Control Volume In addition to methods discussed for closed system, the entropy can be exchanged through mass flows across the boundaries of the control volume.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 The entropy balance in the rate form for a control volume becomes: For a steady‐state steady‐flow process, it simplifies to:



MODULE-I

LECTURE-5

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul AVAILABILITY AND IRREVERSIBILITY

Available Energy

From second law of thermodynamics we found that complete conversion of heat into work is not possible in a continuous process. Also it has been proved that the most efficient cycle to produce work is a reversible powerEven in Carnot cycle, the efficiency of conversion can never be unity and hence to establish a comparison of the workmaximum theoretical work obtainable with respect to some datum must be determined. This chapter is dedicated for this objective

The sources of energy can be divided into two groups namely, highenergy and low-grade energy. The conversion of highis exempt from the limitations of the second law, while conversion of low gradeenergy is subjected to them.

High grade energy: 1) Mechanical work 2) electrical energy 3) water power 4) wind power 5) kineticLow grade energy: 1) Heat or thermal energy 2) heat derived fromor fusion. 3) Heat derived from combustion of fossil fuels. 4)by Prof. (Dr.) Manmatha K. Roul AVAILABILITY AND IRREVERSIBILITY

From second law of thermodynamics we found that complete conversion of heat into work is not possible in a continuous process. Also it has been proved that

efficient cycle to produce work is a reversible power cycle (Carnot cycle). arnot cycle, the efficiency of conversion can never be unity and hence to

establish a comparison of the work-energy conversion in actual processes, the l work obtainable with respect to some datum must be

determined. This chapter is dedicated for this objective. The sources of energy can be divided into two groups namely, high

grade energy. The conversion of high-grade energy to shaftexempt from the limitations of the second law, while conversion of low grade

energy is subjected to them. 1) Mechanical work 2) electrical energy 3) water power 4)

wind power 5) kinetic energy of a jet 6) tidal power.Low grade energy: 1) Heat or thermal energy 2) heat derived from nuclear fission or fusion. 3) Heat derived from combustion of fossil fuels. 4) Solar energy. Page 2 From second law of thermodynamics we found that complete conversion of heat into work is not possible in a continuous process. Also it has been proved that

cycle (Carnot cycle). arnot cycle, the efficiency of conversion can never be unity and hence to

energy conversion in actual processes, the l work obtainable with respect to some datum must be

The sources of energy can be divided into two groups namely, high-grade grade energy to shaft work

exempt from the limitations of the second law, while conversion of low grade

1) Mechanical work 2) electrical energy 3) water power 4) energy of a jet 6) tidal power.

nuclear fission energy.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 The high-grade energy in the form of mechanical work or electrical energy is obtained from sources of low-grade energy. The complete conversion of low grade energy, heat in to high-grade energy, shaft work is impossible. That part of low-grade energy which is available for conversion is referred to as available energy, while the part which according to the second law must be rejected is known as unavailable energy.

Heat transfer from a constant temperature energy source.

In the previous chapter the concept of efficiency of a device such as turbine, nozzle and compressor are introduced and more correctly termed as first law efficiency, since it is given as the ratio of two energy terms. This chapter gives more meaningful definition of efficiency- second law analysis. Our main goal is to use this analysis to manager our thermal resources and environment better.

Consider the simple situation shown in figure1 in which there is an energy source Q in the form of heat transfer from a very large source and therefore constant temperature reservoir at temperature T. what is the ultimate potential for producing work?

To answer to this question we imagine that a cyclic heat engine is available as shown in figure (b) to convert the maximum fraction of Q requires that the engine be completely reversible, i.e. a Carnot cycle, and that the lower temperature reservoir be at the lowest temperature possible, often but not necessarily at the ambient temperature. From the first and second laws for the Carnot cycle and the usual consideration of all the Q’s as positive quantities we find

The fraction of Q given by the right side of the equation is the available portion of

the total energy quantity Q.

Consider the situation shown on the T-S Diagram.

The total shaded diagram is Q.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 The portion of Q that is below To, the environment temperature, can not be converted into work by the heat engine and must instead be thrown away. This portion is therefore the unavailable portion of the energy Q, and the portion lying between the two temperatures T and To is the available energy.

Fig : T-s Diagram for a constsnt temperature energy source

Let us consider the same situation except that the heat transfer Q is available from a constant pressure source, for ex, a simple heat exchanger as shown in the figure. The Carnot cycle must now be replaced by a sequence of such engines, with the result shown in the figure B the only difference between the first and the second example is that the second includes an integral, which corresponds to S

Note that this S quantity does not include the standard sign convention. It corresponds to the change of entropy. The equation specifies the available portion

Prepared by Prof. (Dr.) Manmatha K. Roul Page 5 of the quantity Q. the portion unavailable for producing work in this circumstance lies below T0.

Thus the unavailable energy is the product of lowest temperature of heat rejection and the change of entropy of the system during the process of supplying heat.

Fig : changing temperature energy source

Decrease in available energy when the heat is transferred through a finite

Temperature difference:

Whenever heat is transferred through a finite temperature difference there is a decrease in the availability of the energy so transferred. let us consider a reversible heat engine operating between T1 and To as shown in the figure


Let us now assume that q1 is transferred through a finite temperature difference

from the reservoir or source at T1 to the engine absorbing heat at T’1 lower than

T1 as shown in the figure


Fig. 5 constant temperature energy source

The availability of Q1 as received by the engine at T’1 and to receiving Q1 and

rejecting Q’2.

Q1 = T1∆ S = T ’1 ∆S’

T1 > T ’1, Hence∆ S’ >∆S

Q2 = Tc∆S and Q‘2 = To∆ S’

Since S’ >S hence Q’2 > Q2

And hence W = Q1- Q’2 = T’1 ∆S’ - To∆ S’

Prepared by Prof. (Dr.) Manmatha K. Roul Page 8 And W = Q1 – Q2 = T1∆S – To∆ S

Hence W’ < W since Q’2 > Q2.

Available energy lost due to irreversible heat transfer through finite temperature difference between source and working fluid during heat addition process is given by

W- W’ = Q’2 - Q2 = To (∆S’ -∆ S)

or decrease in AE = To (∆S’ -∆ S)

Thus the decrease in available energy is the product of the lowest feasible temperature of heat rejection and the additional entropy change in the system while receiving heat irreversibly compared to the case of reversible heat transfer from the same source. The greater is the temperature difference (T1 – T’1) the greater is the heat rejection Q’2 and greater will be the unavailable part of the energy supplied. Energy is said to be degraded each time when it flows through a finite temperature difference. That’s why the second law is sometimes called the law of degradation of energy and the energy is said to run down hill.



MODULE-I

LECTURE-6

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 AVAILABLE AND UNAVAILABLE ENERGY:-

The energy content of a system can be divided into two parts

1. Available energy, which under ideal conditions may be completely converted into work

2. Unavailable energy which is usually rejected as waste.

Consider Q units of heat energy available at a temperature T. Available part of energy can be obtained by assuming that the heat is supplied to a Carnot engine.

Work obtained from the carnot engine QT

TT o − is the available part. The quantity

QT

To is the unavailable part. In a T-S diagram these quantities can be represented

as shown in the fig 6.1. The term T0 is the ambient temperature. Hence it can be concluded that the available and unavailable part of energy content of a system depends on the ambient conditions also.

Reversible Work In A Non-flow Process:-

From first law of thermodynamics

Qsys- ∆W=U2- U1

From second law of thermodynamics for a reversible process

(∆s) universe = (∆s)system + (∆s) surroundings = 0

Where (∆s) system =S2- S1

(∆s)surroundings=o

Sys

Surr

surr

T

Q

T

Q −=

Where, Qsystem = To(S2-S1)

Substituting in equ we get To(S2-S1) - W=U2- U1 ∴ W= (U2− U1) − (S1− S2)

since the process is reversible W can be represented Wrev

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 ∴ Wrev= (U1− U2) − To(S1− S2)

This is also the maximum work in the process.

For a closed system, when undergoing change in volume, the work done against the atmospheric pressure:

Watm=po(V2 − V1)

But this work is not an useful work and hence Wmax,useful= Wmax− Watm

= [(U1 − U2) − To(S1 − S2)]− po(V2− V1)

= (U1 − U2) + Po(V1 − V2)]− To(S1− S2)

Reversible Work In A Steady-state Control Volume Steady flow energy equation for a constant volume is

for a single inlet and outlet

From Second law of thermodynamics

∆sun= (∆s)cv + (∆s)surr =0 Where

Substituting these values we get

++− ++=− ∑∑ gZC

hmgZC

hmWQin

in

out

outrev 22

22

&&&& ( ) ( ) −+ −+−=− 12

21

22

12 2ZZg

CChhmWQ rev

&&& ( )[ ]12 ssmsCV −=∆ &

o

SurT

Qs

&−=∆

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 neglecting kinetic and potential energy changes In an open system a fixed volume in space known as control volume is taken for analysis. Hence the atmospheric work term po(V1-V2) should not be considered. Therefore

Wrev= Wmax,useful for an open system ( )( )12

12

ssmTQ

T

Qssm

o

o−= =−&&

&

& ( ) ( )[ ]2121 ssThhmW orev −−−= &&



MODULE-I

LECTURE-7

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Availability

The maximum useful work that can be obtained from the system such that the system comes to a dead state, while exchanging heat only with the surroundings, is known as availability of the system. Here the term dead state means a state where the system is in thermal and mechanical equilibrium with the surroundings. Therefore for a closed system availability can be expressed as ( ) ( ) ( )ooooo SSTVVpUU −−−+−=φ Similarly for an open system ( ) ( )ooo SSTHH −−−=ψ In steady flow systems the exit conditions are assumed to be in equilibrium with the surroundings. The change in availability of a system when it moves from one state to another can be given as: For a closed system ( ) ( ) ( )21212121 SSTVVpUU oo −−−+−=−φφ For an open system ( ) ( )212121 SSTHH o −−−=−ψψ . Availability Change Involving Heat Exchange with Reservoirs:- Consider a system undergoing a change of state while interacting with a reservoir kept at TR and atmosphere at pressure po and temperature To. Net heat transfer to the system Qnet= QR-QO. From first law of thermodynamics Qnet- Wrev=U2-U1 ...6.12 From second law of thermodynamics, assuming the process to be reversible

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 (∆s)Res+(∆s)atm+(∆s)sys=0 ( ) 012 =−++− SSTQ

TQ

o

o

R

R The negative sign for QR shows that the heat is removed from the reservoir. By rearranging We get ( )21 SSTTTQQ o

R

oRo −+= Net heat transferred Qnet =QR-Qo ( )21 SST

TTQQQ o

R

oRRnet −−−= Susbstituting the values in the equation ( ) 1221 UUWSST

TTQQ revo

R

oRR −=−−−− ( ) −+−−−=

R

oRorev T

TQSSTUUW 12121 ( ) ( ) −+−−−+−=R

oRoouseful T

TQSSTVVpUUW 1212121max, Irreversibility :- Work obtained in an irreversible process will always be less than that of a reversible process. This difference is termed as irreversibility (i.e) the difference between the reversible work and the actual work for a given change of state of a system is called irreversibility. I=Wrev− Wact

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 Let a stationary closed system receiving Q kJ of heat is giving out Wact kJ of work. From first law of thermodynamics, Q - Wact = U2− U1 Wact = U1− U2+Q Wrev =(U1− U2) − TO(S1− S2) = (U1− U2) + T0(∆s)system ∴ I = Wrev− Wact = (U1− U2) + T0(∆s)system− (U1- U2) − Q = T0(∆s)system− Q Where Q = − Qsurroundings = TO(∆s)surroundings = T0(∆s)system+TO ∆ssurroundings =T0(∆s)universe Since (∆s)universe will be positive for an irreversible flow, irreversibility will be zero for a reversible process and will never be negative. I ≥ 0 Similarly for a steady flow system I=Wrev− Wact Where Qsys= Qo= TO ∆ssurroundings Therefore I = T0 (S1− S2) + TO ∆ssurroundings = T0 [∆ssys +∆ssurroundings] = T0 [∆suniverse] ( ) ( )[ ]( )[ ] sysact

orev

QhhmWssThhmW +−= −−−= 21 2121

&

&&

Prepared by Prof. (Dr.) Manmatha K. Roul Page 5 Second Law efficiency: With the increased use of availability analysis in recent years a term called second law efficiency has come into more common use. This term refers to comparison of the desired output of a process with the cost or input in terms of the thermodynamic availability. Thus the isentropic turbine efficiency defined by the ratio of actual work output to the work for a hypothetical isentropic expansion. From the same inlet state to the same exit pressure which is called first law efficiency, in that it is a comparison of two energy quantities. The second law efficiency as just described would be the actual work output of the turbine divided by the decrease in availability from the same inlet state to the same exit state. Thus the second law efficiency is Where (ψ1 -ψ 2) is the decrease in availability for a steady state steady flow process, which is equal to the reversible work or maximum work obtainable. In this sense this concept provides a rating or measure of the real process in terms of the actual change of state and is simply another convenient way of utilizing the concept of thermodynamic availability. In a similar manner the second law efficiency of a pump or a compressor is the ratio of the increase in availability to the work input to the device.



MODULE-I

LECTURE-8

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Vapour Power cycle Introduction: An important application of thermodynamics is the analysis of power cycles through which the energy absorbed as heat can be continuously converted into mechanical work. A thermodynamic analysis of the heat engine cycles provides valuable information regarding the design of new cycles or for improving the existing cycles. Classification of Cycles: The purpose of a thermodynamic cycle is either to produce power, or to produce refrigeration/pumping of heat. Therefore, the cycles are broadly classified as follows: (a) Heat engine or power cycles. (b) Refrigeration/heat pump cycles.

Power cycles:- Any thermodynamic cycle is essentially a closed cycle in which, the working substance undergoes a series of processes and is always brought back to the initial state. Different types of working fluids are employed in the power plants. The nature of the working fluids can be classified into two groups: vapours and gases. The power cycles are accordingly classified into two groups as: 1) Vapour power cycles: - in which the working fluid undergoes a phase change during the cyclic process. (2) Gas power cycles:- in which the working fluid does not undergo any phase change. Vapour power cycles:- Power plants work on a cycle that produces net work from a fossil fuel (natural gas, oil, coal) nuclear, or solar input.

For Vapor power plants the working fluid, typically water, is alternately vaporized and condensed.

Schematic diagram:-


SIMPLE LINE DIAGRAM:-

Rankine Cycle: Rankine cycle is the ideal working cycle of a steam power plant - The simple Rankine cycle has the same component layout as the Carnot Cycle shown above. The simple Rankine cycle continues the condensation process 4-1 until the saturated liquid line is reached.

Steam Power Cycle Turbine 2 Pump Condenser Wturb 1 3 QI Qout 4 Boiler Wp

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 Ideal Rankine Cycle Processes Process Description 1-2 Isentropic Expansion in Turbine 2-3 Constant Pressure Heat Rejection in Condenser 3-4 Isentropic Compression in Pump

4-1 Constant Pressure Heat Addition in Boiler

T-s and h-s diagram and p-v diagram

Cycle analysis:- Considering each process separately and applying conservation of energy to each control volume

1�2 Turbine (adiabatic expansion)

Prepared by Prof. (Dr.) Manmatha K. Roul Page 5 )(0 21 hhm

W

m

Q out −+−=&

&

&

&

)( 21 hhm

Ww outout −==

&

&

2�3 Condenser (no work)

)(0 32 hhm

W

m

Q out −+−−

=&

&

&

&

)( 32 hhm

Qq outout −==

&

&

3�4 Pump (Adiabatic)

)(0 43 hhm

W

m

Q in −+−

−=&

&

&

&

)( 34 hhm

Ww inin −==

&

&

4�1 Steam Generator (no work)

)(0 14 hhm

W

m

Q in −+−=&

&

&

&

)( 41 hhm

Qq inin −==

&

&

Thermal Efficiency of a simple Rankine cycle:-

Thermal efficiency=�� =��

3 4 )(−inW

& 2 3 )(−outQ& 1 4 )(+inQ&

41

3421 )()(hh

hhhhRankine

−

−−−=η

Prepared by Prof. (Dr.) Manmatha K. Roul Page 6 Back Work Ratio (bwr) :-

21

34

//

(turbine)output work (pump)input work

hh

hhbwr

w

w

mW

mWbwr

out

in

out

in

−

−=

===&&

&&

Steam rate:- It is defined as the rate of steam flow (kg/hr) required for producing unit shaft output (1 kW), therefore, Steam Rate =�� (kg/KWH) Heat Rate: - It is rate of heat input (Qin) required for producing unit work output (1 kW).

Heat Rate=��"� (kJ/KWH) where Qin is added for kg of steam

ENGINEERING THERMODYNAMICS MODULE-I LECTURE-1 · the Rankine cycle efficiency, The reheat cycle,...

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Transcript of ENGINEERING THERMODYNAMICS MODULE-I LECTURE-1 · the Rankine cycle efficiency, The reheat cycle,...