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ENGINEERING SUPPORT PERSONNEL TRAINING PROGRAM

FUNDAMENTALS

Thermal Sciences

ESP100.30 Rev. 4 Chapter 1 Basic Thermodynamics

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THERMAL SCIENCE

STUDY GUIDE

ESP100.30 Rev. 4

ENGINEERING FUNDAMENTALS

HEAT TRANSFER AND FLUID FLOW

Chapter 1 Basic Thermodynamics

Chapter 2 Properties of Heat Transfer

Chapter 3 Heat Transfer and Heat Exchanger

Chapter 4 Reactor Heat Transfer

Chapter 5 Frictionless Fluid Flow

Chapter 6 Actual Fluid Flow

Chapter 7 Pumps and Fluid System Response


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TABLE OF CONTENTS

Page List of Figures .............................................................................................................................................. iii Enabling Objectives ..................................................................................................................................... iv Introduction ................................................................................................................................................ 1-1 Units and Properties ................................................................................................................................... 1-2

Units ............................................................................................................................................... 1-2 Properties and State of a Substance ............................................................................................... 1-2 Temperature Change (Delta T) ...................................................................................................... 1-8

Specific Heat Equation............................................................................................................................... 1-8 Heat of Fusion and Heat of Vaporization .................................................................................................. 1-9

Sensible and Latent Heat.............................................................................................................. 1-12 Properties Derived from General Laws ................................................................................................... 1-12

Internal Energy (U) ...................................................................................................................... 1-12 Enthalpy (H)................................................................................................................................. 1-12 Entropy (S) ................................................................................................................................... 1-13

Specific Properties ................................................................................................................................... 1-14 Specific Enthalpy (h) and Specific Entropy (s) ........................................................................... 1-14 Specific Weight (w) ..................................................................................................................... 1-15 Specific Gravity (sg) .................................................................................................................... 1-15

The Thermodynamic System ................................................................................................................... 1-16 Fluid ............................................................................................................................................. 1-16 System Boundaries....................................................................................................................... 1-16 Closed System.............................................................................................................................. 1-16 Open System ................................................................................................................................ 1-16 Steady State, Steady Flow System............................................................................................... 1-17 Working Fluid .............................................................................................................................. 1-17 State of a System.......................................................................................................................... 1-17


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Phase of a System ........................................................................................................................ 1-17 Equilibrium .................................................................................................................................. 1-18 Process ......................................................................................................................................... 1-18 Cycle ............................................................................................................................................ 1-19 Energies of The Thermodynamic System.................................................................................... 1-19

Summary .................................................................................................................................................. 1-26 Definitions................................................................................................................................................ 1-28 Exercises .................................................................................................................................................. 1-30


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LIST OF FIGURES

Page Figure 1.1 Gage and Absolute Pressures 1-5

Figure 1.2 Data for Examples A and B 1-6 Figure 1.3 Temperature versus Heat Added to Water at Atmospheric Pressure 1-10

Figure 1.4 Expansion of Compressed Gas Leaking to Atmosphere 1-18 Figure 1.5 Potential Energy 1-20

Figure 1.6 Specific Heat of Water at Different Pressure 1-25


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1.0 Enabling Objectives

1.1 Summarize the concept of each of the following terms as presented in the text, including the appropriate English System unit(s) of measurement (where applicable)

• Intensive properties

• Extensive properties

• State of a system

• Phase of a system

• Volume and specific volume

• Density

• Enthalpy and specific enthalpy

• Entropy and specific entropy

• Temperature

• Specific gravity

• Pressure

• Velocity

• Specific heat capacity

• Heat of vaporization and heat of fusion

1.2 Given a temperature in either one of the following temperature scales, convert it to the other scale:

• Fahrenheit

• Rankine

1.3 Given the specific heat equation, solve problems involving heat, mass, temperature difference, initial temperature, and final temperature.

1.4 State the limitations of the specific heat equation.


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1.5 Given values of two (2) of the following quantities, calculate the third.

• heat

• mass

• heat of vaporization

1.6 Compare the term’s open and closed systems.

1.7 Predict the temperature and phase of water as a result of sensible and latent heat being added to the water.


1.1

1.0 Introduction

In thermodynamics, a working substance is any fluid (including gases) which receives, transports, and transfers energy in a system. The state or condition of a working substance at any location in any system may be determined if the thermodynamic properties of the substance at the location of interest are known. These properties include: • Pressure • Temperature • Density (and Specific Volume) • Internal Energy • Enthalpy • Entropy There are three basic phases in which a fluid may exist: solid, liquid, or gas. A fluid may exist in a combination of these phases such as a solid-liquid combination or a liquid-vapor (gaseous) combination’ the state in which it exists is specified by its thermodynamic properties such as pressure, temperature, volume, etc. At least two properties of the fluid must be known in order to specify its state of existence. Distinguishing characteristics of the three phases can be summarized as follows:

Solid Liquid Gas

Definite volume Definite volume Indefinite volume

Definite shape Indefinite shape Indefinite shape

Molecules in fixed position Molecules can move and interact with each other

Molecules move independently

Lowest energy per molecule Intermediate energy per molecule

Highest energy per molecule

It should be emphasized that temperature is proportional to the average kinetic energy per molecule, and therefore is related to the phase as demonstrated in the case of the three phases of water. The other properties will be discussed in the following sections.


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1.1 Units and Properties

1.1.1 Units

Throughout this course, the English Engineering system of units (ft-lb-sec) is used to express fluid properties. The fourth unit used in the English system is the °F, which we use as an arbitrary measure of temperature. Temperature is also a thermodynamic property. The thermodynamic properties are then all derived, or defined, in terms of these four basic units.

1.1.2 Properties and State of a Substance If we consider a given mass of water, we recognize that this water can exist in various forms. If it is a liquid initially, it may become a vapor when it is heated, or a solid when it is cooled. Thus we speak of the different phases of a substance. A phase is defined as a quantity of matter that is homogeneous throughout. When more than one phase is present, the phases are separated from each other by the phase boundaries. In each phase, the substance may exist at various pressures and temperatures or, to use the thermodynamic term, in various states. The state may be identified or described by certain observable, macroscopic properties; some familiar ones are temperature, pressure, and density. Property is defined as an observable or measurable characteristic of a system’s behavior. Each of the properties of a substance in a given state has only one definite value, and these properties always have the same value for a given state, regardless of how the substance arrived at that state. In fact, a property can be defined as any quantity that depends on the state of the system and is independent of the path (i.e., the prior history) by which the system arrived at the given state. Thermodynamic properties can be divided into two general classes, intensive and extensive properties. An intensive property is independent of the mass; the value of an extensive property varies directly with the mass. Thus, if a quantity of matter in a given state is divided into two equal parts, each part will have the same value of intensive properties as the original, and half the value of the extensive properties. Pressure, temperature, and density are examples of intensive properties. Mass and total volume are examples of extensive properties. Extensive properties per unit mass, such as specific volume, are intensive properties. The basic properties of the working fluid in an energy transfer system are fundamental to understanding the operation of such a system. Some of these properties, such as mass, volume, temperature and pressure, are familiar concepts and can be defined directly.


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Mass (m) and Weight (W)

The mass of a body is the measure of the amount of material present in that body. The weight of a body is the force exerted by that body when its mass is accelerated in a gravitational field. Frequently mass and weight are said to be equivalent; however, this is not true as demonstrated by Newton’s second law.

Force (F) = mass (m) x acceleration (a)

The weight of a body is actually a force produced when the mass of the body is accelerated by a gravitational acceleration. The mass of a certain body will remain constant even through the gravitational acceleration acting upon that body changes. For example, on earth an astronaut has a certain mass and a certain weight. When the same astronaut is placed in outer space away from the earth’s gravitational field, his mass is the same but he is now in a “weightless” condition (i.e., gravitational acceleration and thus force approaches zero). The English system uses the pound (lbf) as the unit of weight. Knowing that acceleration has the units of ft/sec2 and using the formula above, we can show that the units of mass are lbf-sec2/ft. The unit of mass generally used is the pound mass (lbm). In order to allow lbm to be used as a unit of mass, we must divide Newton’s second law by a conversion factor known as the gravitation constant.

This results in Newton’s second law as follows:

where mass (m) is expressed in lbm. If we are on the surface of the earth, (a) is equal in magnitude to the gravitational constant (g) and we can now provide that for the systems that we analyze 1 lbm exerts 1 lbf:


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1.1.2.2 Volume (V) The volume of a system is a measure of the room that it occupies in space. Volume may be calculated by measuring the dimensions of the system or by measuring the volume of gas or liquid that the system would displace. The shape of a system determines how its volume can be calculated by measuring dimensions. The units of volume used in the English system are:

ft3 in3 gallon 1.1.2.3 Velocity (v) The velocity of a system or substance moving through a system is the distance traveled per unit of time. The units of velocity that we will encounter are:

Note: velocity and speed are used interchangeably in this text. 1.1.2.4 Pressure (P) The pressure of a system is the force per unit area exerted by the system on its surroundings. This force acts in all directions, but the pressure can be calculated by taking the total force in one direction and dividing it by the area of the system surface perpendicular to the direction of the force. The units of pressure are pounds-force per square inch (lbf/in2), commonly written psi, or pounds-force per square foot (lbf/ft2).

(where)

As an example, let us calculate to what pressure (in psi) you must inflate the tires of a 3,000-lb car.


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Assume area of tire contact with the road is: 25 in2.

Pressure gages read pressures above the atmospheric pressure. The pressures are read as psig (lbf/in2 gage). Conversely, pressures below atmospheric pressure are measured with vacuum gages. These gages measure the amount the pressure is below the atmospheric pressure. Vacuum pressures can be measured in psi vacuum or in terms of the height of a column of mercury (inches Hg vacuum). In order to have a reference point for all types of pressure measurements, the absolute pressure is used. Absolute pressure is defined as the pressure relative to the pressure existing in a perfect vacuum (P=0). Figure 1.1 shows these relationships diagrammatically.

FIGURE 1.1 GAGE AND ABSOLUTE PRESSURES


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The following formulas show the relationship between the various ways of expressing pressure.

EXAMPLE A A gage on a main steam line indicates 25.3 psig. Determine the absolute pressure. Refer to Figure 1.2. Solution

FIGURE 1.2 DATA FOR EXAMPLES A AND B


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EXAMPLE B A vacuum gage on the main condenser reads 13.0 psiv. Determine the absolute pressure. Refer to Figure 1.2. SOLUTION

EXAMPLE C A mercury manometer on a tank indicates 31.1 Hg above atmospheric pressure. Determine the absolute pressure. SOLUTION

1.1.2.5 Temperature (°F) Temperature defines the energy stored or contained in a substance. Temperature is normally measured with a thermometer scale calibrated in degrees Fahrenheit. However, the information it indicates is only relative thermal energy content. To obtain a measure of the absolute thermal energy content of a substance, it is necessary to establish a temperature reference at which the energy content is zero. Such a reference has been established as absolute zero, which is equated to -460°F. The Fahrenheit scale has the freezing point of water defined as 32°F. On this scale, absolute zero is at -460°F. On the Rankine scale, the temperature at absolute zero is 0°R. A temperature change of one degree Fahrenheit is equal to a temperature change of one degree Rankine. The relationship between the Rankine TR and Fahrenheit TF scale is:


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1.1.3 Temperature Change (Delta T) Heat input to a mass generally causes an increase in temperature. It is convenient to shorten the mathematical notation by using the symbol (Greek letter) to represent a change or a second condition minus a first condition. Thus, T may be used to represent a second temperature minus a first temperature, or a high temperature minus a low temperature.

1.2 Specific Heat Equation Heat (Q) is an energy in transition. If this heat is supplied to a mass, m, it causes the mass to rise in temperature from T1 to T2. This may be expressed by the Specific Heat Equation:

where cp is a value called specific heat (heat capacity) at constant pressure, having units BTU that make the equation dimensionally consistent. lbm °F For example,

where:

For gases the process must be specified: cp - specific heat at constant pressure (isobaric) cv - specific heat at constant volume (isometric) For solids and liquids, however, the difference between cp and cv is insignificant and the process is not generally considered. As a matter of convention, however, the symbol cp is used for heat transfer processes involving solids and liquids.


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If, in the specific heat equation, the mass is taken as 1 lbm of water, the specific heat cp at atmospheric pressure is (normally taken as)

and the temperature difference T is taken as 1°F, the specific heat equation defines the BTU heat unit. The BTU is the amount of heat required to raise one pound mass of water by 1°F. Similarly, in the old metric system the calorie is the amount of heat required to raise one gram of water 1°C.

In the new SI (French, Système Internationale) metric system the BTU is defined in terms of the joule and the watt.

Often in the PWR, heat is being transferred to a flowing mass of water, rather than a stationary mass. In this case, the mass is expressed in terms of mass flow rate (m). Thus, the specific heat equation transforms to:

Note: The specific heat equation , has a distinct limitation in that it cannot be used where there is a change of phase. Equations relating heat transfer to changes in enthalpy (as will be presented later) should be used in those situations. 1.3 Heat of Fusion and Heat of Vaporization Heat supplied to a substance causes its temperature to rise with an increase in internal energy until it reaches the temperature of fusion or evaporation. When the temperature of fusion is reached, the heat of fusion causes the substance to change from a solid to a liquid at the temperature of fusion. When the temperature of vaporization or boiling (called saturation temperature) is reached, the heat of vaporization (also called latent heat or enthalpy of vaporization) causes the substance to change from a liquid to a vapor (gaseous form) at the vaporization temperature.


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At atmospheric pressure:

FIGURE 1.3 TEMPERATURE VERSUS HEAT ADDED TO WATER AT ATMOSPHERIC PRESSURE


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Figure 1.3 illustrates the effect of adding heat to water. For ice at a temperature below 32°F, any heat added results in a temperature increase of the ice until its temperature reaches 32°F. Notice that as heat continues to be added to the ice, its temperature does not change. The melting process is a constant temperature process, also referred to as an isothermal phase change. Notice also that the boiling process (which begins when the water is a 212°F at atmospheric pressure) is an isothermal phase change process. where:

The amount of energy gained or lost during the transition between the solid and liquid phases or the liquid and vapor phases is calculated from the relationship.

The symbol hfg represents either the heat of fusion or the heat of vaporization of the material. The value of the heat of vaporization depends on the pressure. EXAMPLE D Determine the amount of heat required to vaporize 5-lb of water at boiling temperature in the pressurizer. The heat of vaporization in the pressurizer during normal operating conditions is 414.8 BTU/lbm. Solution


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1.3.1 Sensible and Latent Heat Two words used to describe heat additions and rejections are sensible and latent. Sensible heat addition (or rejection) is one in which the substance experiences a change in temperature, but not a change in phase. Referring to Figure 1.3, heat added between 0 and Q1, Q2 and Q3, and Q4 and beyond is sensible heat. Latent heat addition is one in which the substance experiences a change in phase, but not a change in temperature. Again referring to the figure, heat added between Q1 and Q2 and between Q3 and Q4, is latent heat. 1.4 Properties Derived from General Laws In addition to observable properties and mathematically derived properties, there exist two properties which are derived from the two general laws* of thermodynamics. These properties, internal energy derived from the first law, and entropy derived from the second law, are not observable properties nor can they be arrived at by mathematical manipulation of other properties. They can be shown to be properties only through the use of the general laws of thermodynamics. They are introduced at this point only to make the list of thermodynamic properties more complete. We also want to show how internal energy is used to define enthalpy, which is also a thermodynamic property. 1.4.1 Internal Energy (U) Internal energy is a motion energy stored in the individual molecules of a substance. Internal energy depends on temperature and the phase of the substance such as solid, liquid or gas. Some steam tales list internal energy values. Internal energy values are useful for the solution of non-flow problems, but in nuclear power plants most problems deal with flow. The thermodynamic property involved in flow problems is enthalpy which is the sum of internal energy and flow energy. Enthalpy is discussed in a following section. Internal energy has units of BTUs as do all forms of energy. 1.4.2 Enthalpy (H) A fluid moving in steady flow transports energy in the fluid. This energy consists of two parts: (1) internal energy (U) stored in the individual molecules as heat energy and (2) flow energy possessed by the fluid because it is flowing with a pressure (P) and a volume (V). Values of internal energy, pressure and volume of water and steam can be obtained from steam tables (discussed later). However, because these properties of a fluid are involved in steady-flow processes, it is convenient to tabulate their sum in a new property defined as enthalpy.

* Note: The First Law of Thermodynamics simply stated: Energy cannot be created or destroyed; this is also called the Law of Conservation of Energy. The Second Law of Thermodynamics simply stated: All energy received as heat by a heat-engine cycle cannot be converted into mechanical work (some heat must be rejected).


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By definition:

where:

Thus, enthalpy has units of BTUs also. 1.4.3 Entropy (S) Entropy is a mathematical quantity that increases if heat is degraded by allowing it to flow from a high temperature to low temperature without producing mechanical work. Friction, in which mechanical work is converted to heat, also increases entropy. The calculation of entropy involves calculus and is beyond the scope of this module, but is defined by the well-known thermodynamic equation:

where:


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For practical use, entropy values have been calculated and are tabulated in the steam tables along with the other properties. In this module, entropy will be used to define the most efficient process achievable by a turbine. Such a process is one in which entropy does not increase. This is called an isentropic process. In actual turbine processes, due to both mechanical and fluid processes, entropy does increase. Note that since units of entropy are not BTUs, it is not a form of energy. 1.5 Specific Properties To be able to tabulate properties in either a table or graph we must use specific properties: properties with a common denominator of either mass or volume. The most important examples for our purpose are the steam table and the Mollier diagram where lbm is the common denominator for specific enthalpy, specific entropy and specific volume. 1.5.1 Specific Enthalpy (h) and Specific Entropy (s) Specific enthalpy is the sum of internal energy and flow work contained by one pound of water or steam. It has units of BTU/lbm. Specific entropy is the quantity of BTU/°F in a pound of steam or water. It has units of BTU/°F lbm. 1.5.2 Specific Volume (v) and Density (ρ) Specific volume is defined as the volume occupied by a unit mass of the substance. The specific volume v is the total volume of the substance divided by the mass of that volume:

where:


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Density is the reciprocal of specific volume and is defined as the mass of a unit volume of the substance. Both density and specific volume measure the same property, namely how close the molecules or atoms making up a substance are to each other. A high value of specific volume (or low value of density) implies that the molecules or atoms in the substance are relatively far apart. This is true of gases and vapors such as hydrogen, oxygen, and steam. Conversely, a low value of specific volume (or high value of density) implies that the molecules are relatively close together. This is true of liquids and solids such as water and ice. Generally, steam tables such as the C-E steam table give only the specific volume of the substance for a given temperature and pressure. If the density is desired, it can be readily calculated.

where:

1.5.3 Specific Weight (w) Specific weight has the same meaning and use as density, only it is referenced to lbf rather than lbm. Like weight being equal to mass on the surface of the earth, specific weight is equal to density on the surface of the earth. Specific weight has units of lbf/ft3. 1.5.4 Specific Gravity (sg) Specific gravity is a dimensionless ratio. The specific gravity of a substance is the ratio of the density of the substance to the density of pure water (sgx = ρx/ρH2O). The specific gravity of pure water is exactly one; the density of pure water is 62.4 lbm/ft3.


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1.6 The Thermodynamic System A system is a particular portion of the universe, normally a particular quantity of matter or a particular space, which we intend to study directly. Around the system are boundaries that the mind constructs. For example, the free body studied in the Physics module is a system. Free-body systems and thermodynamic systems differ by reason of the ways they are studied. In mechanics, we study the effects of forces associated with a system; whereas in thermodynamics, we study the passage of energy associated with a system, either with or without the passage of matter into or out of the system. 1.6.1 Fluid We think of the working substance of a thermodynamic system as a fluid in which energy can be stored and removed for use in that system. A fluid is any substance that conforms to the shape of its container; it may be liquid or gas. We store energy so that we can bring about a desired energy transformation; for example, transformation of the energy of steam into the energy of a steam turbine, air-fuel mixture into the energy of a diesel engine, and hydraulic fluid into the energy of a jack. Thermodynamics deals especially with the laws of transformation of heat into other forms of energy and vice versa. Various types of energy in a system will be discussed further in the next section. 1.6.2 System Boundaries We should bear in mind that the term “system” as used in mechanical engineering has an infinite range of applications. For example, a working substance or even a certain part of it may be regarded as a system; so may a turbine, a reduction gear, a generator, or any other individual item. Furthermore, any group of items that we enclose by an imaginary line for analysis is regarded as a system; for example, a turbine-generator set or an air conditioner. 1.6.3 Closed System In a closed system, matter does not cross boundaries of the system. Energy may or may not flow into or out of it. A sealed jug of hot or cold water is an example of a closed system; so is a power plant system if we ignore leakage. 1.6.4 Open System In an open system, matter does cross the boundaries. Energy may pass the boundaries either alone or with the flow of mass. A water wheel is an example of an open system; so is a steam turbine.


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1.6.5 Steady State, Steady Flow System A special type of system which is of particular interest is the steady state, steady flow system. In this system, all points remain in a particular condition, and the rate at which mass enters the system is equal to the rate at which mass leaves the system. An operating automobile engine radiator might be a system which experiences steady state, steady flow, if speed is constant. 1.6.6. Working Fluid Thermodynamics is concerned with the transformation of heat energy into more useful forms or to perform work. Very often it is necessary to store energy or to perform several transfers to different systems to achieve these objectives. A substance called a working fluid is used to perform the desired functions. In many cooling systems, water or freon is the working fluid used to transport heat. In a thermodynamic system, the working fluid is used to transport, transform or store energy. 1.6.7 State of a System The state of a working fluid in a system is defined in terms of its thermodynamic properties: pressure, temperature, specific volume, enthalpy, internal energy, and entropy. Only two independent thermodynamic properties are required to completely define the state of the working fluid. If two independent thermodynamic properties are known, the value of each of the remaining properties is unique and can be determined. 1.6.8 Phase of a System A phase is the condition of a system as described by its fluidity. Normally there are three phases in which a substance may exist: • Solid • Liquid – incompressible fluid • Gas – compressible fluid Under certain conditions more than one phase may coexist. For example, water in the pressurizer and condenser exists as two phases: gaseous and liquid.


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Terms for Identifying Change of Phase

• Melting solid to liquid

• Vaporization liquid to gaseous

• Freezing or Solidifying liquid to solid

• Condensation gaseous to liquid

• Sublimation solid to gaseous A change of phase is always accompanied by a change of state, but a change of state may or may not be accompanied by a change of phase. 1.6.9 Equilibrium When the properties of a system do not change throughout the entire system, the system exists in a state of equilibrium. If the temperature is uniformly distributed through a system, then the system is in thermal equilibrium. Mechanical equilibrium relates to pressure. If the pressure at various points throughout the system is not changing with time, then the system is in mechanical equilibrium. Pressure does vary due to gravitational effects according to the hydrostatic pressure principle; however, these slight variations in pressure have very little effect on the overall thermodynamic analysis. Finally, if the state of a system (the properties of a system) does not change throughout the system, then the system is in thermodynamic equilibrium. 1.6.10 Process The term “process” is used to express the state path that is formed when the properties of a system change. See Figure 1.4.

FIGURE 1.4 EXPANSION OF COMPRESSED GAS LEAKING TO ATMOSPHERE

EXPANDED GAS COMPRESSED

GAS


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A process occurs whenever a system changes from one state to another. The gradual cooling of coffee in a thermos jug is a process because it results in a changing property of the system, namely, temperature. In addition to designating a process by the property which changes, processes can be characterized by the fact that certain properties do not change. An isothermal process is one in which temperature remains constant. A process is designated isobaric if pressure remains constant, isometric if volume remains constant, and adiabatic if no heat is transferred. 1.6.11 Cycle A cycle is a series of processes which periodically results in a final state of a system which is identical to the initial state of the system before the series of processes was begun. 1.6.12 Energies of The Thermodynamic System 1.6.12.1 Energy Energy is defined as the capacity of a system to perform work or produce heat. Although it is difficult to define energy in a general sense, it is easy to define it in terms of the work done by or on a system. The concept that a system possess a certain quantity of energy which is decreased when the system performs work and increased when work is done on the system is fundamental to understanding energy transfer systems. When the working fluid performs work, its energy is decreased; when work is done on it, its energy is increased. There are many different forms of energy, such as mechanical energy, thermal energy, electrical energy, chemical energy, and nuclear energy. The total energy of a substance is the sum of the magnitudes of the various forms of energy the substance possesses. Normally, the total amount of energy a body possesses cannot be determined in an absolute sense. It must be measured with respect to some reference. Thus, the potential energy of a pound of water is defined in terms of its position above some reference position. This approach is satisfactory for most engineering applications since the change in energy is what relates to the work done. Four forms of energy possessed by the working fluid in an energy transfer system are important in the analysis of such systems: (1) potential energy, (2) kinetic energy, (3) internal energy, and (4) flow energy. They can all be measured in any units of energy, e.g., BTUs or ft-lbf. 1.6.12.2 Potential Energy (PE) Potential energy exists because of some vertical distance (z) over which gravitational force (g) can be exerted on a system’s mass (m/gc). The product (mg/gc) has units of pounds-force and z is in feet. Thus, potential energy has units of ft-lbf. We can calculate the potential energy change due to a body falling or being raised. A weight at some distance above the floor will give up a certain amount of energy upon impact if it is allowed to fall freely to the floor.


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For the process of falling, the change in mechanical potential energy of the body as it falls is equal in foot-pound units to the w in pounds times the distance z in feet through which it falls. Thus, the mechanical potential energy PE is mgz/gc, ft-lbf, where z is the elevation above the reference point. In general, if the body moves from an elevation Z1 to an elevation Z2, the change in potential energy is:

But,

Therefore,

Observe that the equation gives a negative number for a decrease or loss of potential energy (PE2 < PE1). See Figure 1.5

FIGURE 1.5 POTENTIAL ENERGY


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If the height of a body above a reference point is decreased, the change of potential energy is negative. On the other hand, if the height of a body above a reference point is increased, the change of potential energy is positive. 1.6.12.3 Kinetic Energy (KE) Kinetic energy is energy of motion. A system has kinetic energy with respect to some point above reference. The kinetic energy of a system is equal to one half the product of the mass and the square of the velocity of the system. Since velocity is relative to some reference point, the kinetic energy of a system is relative to its reference point. The expression of the total energy supplied is:

in which:

This equation is applicable to moving fluids (liquids or gases) as well as to rigid bodies. To illustrate that KE has the same units as PE, we will work the following example. EXAMPLE E Determine the kinetic energy of 1bm of steam flowing through a pipe at a velocity of 100 ft/sec. SOLUTION


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1.6.12.4 Internal Energy (U) Potential energy and kinetic energy are macroscopic forms of energy. They can be visualized in terms of the position and the velocity of the total system. In addition to these macroscopic forms of energy, a substance possesses several microscopic forms of energy. These are due to the rotation, vibration, translation and interactions among the molecules of the substance. Each of these forms of energy cannot be evaluated directly, but techniques have been developed to evaluate the change in the total sum of all these microscopic forms of energy. This sum of energy is called the internal energy. It is customarily represented by the symbol U. In engineering applications, the unit of internal energy is the British thermal unit (BTU), which is also the unit of heat. The specific internal energy u of a substance is its internal energy per unit mass. It equals the total internal energy U divided by the total mass m.

where:

1.6.12.5 Flow Energy (PV) In addition to the internal energy U, there is another form of energy which the working fluid of an energy transfer system possesses that is important in understanding such a system,. The work done on the working fluid as it moves from one point in a system to another is called PV or flow energy. It is numerically equal to PV, pressure times volume.

Energy is defined as the capacity of a system to perform work. If a system with pressure and volume is permitted to flow, it will move from one point to another. Thus a fluid under pressure has the capacity to perform work (movement of the fluid). This is energy. In engineering applications, the units of PV energy are the units of pressure times volume, pounds-force per square foot times cubic feet, which equals foot-pounds-force (ft-lbf).


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1.6.12.6 Work and Heat Kinetic energy, potential energy, internal energy and PV energy are forms of energy that are all properties of the system. Work and heat also are forms of energy, but they are energy in transit. They are not properties of the system. Work is done by or on a system, but a system contains no work. Likewise, heat is transferred to or from a system, but a system contains no heat. The distinction between the forms of energy that are properties of a system and the forms of energy that are transferred to and from a system is fundamental to the understanding of energy transfer systems. 1.6.12.7 Work (W) Work is defined for mechanical systems as the action of a force on an object through a distance. It equals the product of the force (f) times the displacement (d).

where:

In dealing with work in relation to energy transfer systems, it is important to distinguish between work done by the system on its surroundings and work done on the system by its surroundings. Work is done by a system when energy is used to turn a turbine and thereby generate electricity in a generator. Work is done on the system when a pump is used to move the working fluid from one location to another. 1.6.12.8 Heat (Q) Heat is defined as the flow of energy due to a temperature difference. The flow is in the direction of the lower temperature. The best way to quantify the definition of heat is to consider the relationship between the amount of heat added to or removed from a system and the change in the temperature of the system. Everyone is familiar with the physical phenomena that when a substance is heated, its temperature increases, and when it is cooled, its temperature decreases. In review, the heat added to or removed from a substance to produce a change in its temperature is called sensible heat. The units of heat are often defined in terms of the changes in temperature it produces.


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In engineering applications, the unit of heat is the British thermal unit (BTU). As previously defined in this chapter, one BTU is defined as the amount of heat required to raise the temperature of one pound-mass of pure water by one degree Fahrenheit at normal atmosphere pressure. Specifically, this is called the 60 degree BTU, as the 1 degree temperature change is from 59.5 to 60.5°F. Recall that latent heat is the amount of head added to or removed from a substance to produce a change in phase. When this heat is added, no temperature change occurs. There are two types of latent heat for water. The first is the latent heat of fusion. This is the amount of heat added to change phase from a solid to a liquid. The second type of latent heat is the latent heat of vaporization. This is the amount of heat added change phase from a liquid to a vapor. The latent heat of vaporization is sometimes called the latent heat of condensation. The ratio of the heat Q added to or removed from a substance to the change in temperature T produced is called the heat capacity (Cp) of the substance. The heat capacity of a substance per unit mass is called the specific heat (cp) of the substance. The subscript p indicates that the heat capacity and specific heat apply when the heat is added or removed at constant pressure.

Where:

The definition of the BTU is equivalent to saying that the specific heat cp of water is 1 BTU/lbm - °F at normal atmospheric pressure. Actually, the specific heat of water varies with pressure and temperature. Figure 1.6 illustrates how the specific heat of water varies as a function of pressure and temperature.


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FIGURE 1.6 SPECIFIC HEAT OF WATER AT DIFFERENT PRESSURE

1.6.12.9 Enthalpy (H) In the analysis of energy transfer systems, the internal energy U and the PV energy often occur together in expressions describing the energy possessed by the working fluid. The enthalpy H of a substance is defined as the sum of the internal energy and the PV energy.

Where:


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The specific enthalpy h of a substance is its enthalpy per unit mass. It equals the total enthalpy H divided by the total mass m. It also equals the sum of the specific internal energy and the specific PV energy. In many applications, the work enthalpy is used alone to refer to the specific enthalpy in BTU per pound-mass.

where:

Enthalpy is a property of a substance, like pressure, temperature and volume, but it cannot be measured directly. Normally, the enthalpy of a substance is given with respect to some reference value. For example, the specific enthalpy of water or steam is given using the references that the specific enthalpy of water is zero at .01°C and normal atmospheric pressure. The fact that the absolute value of specific enthalpy is unknown is not a problem, however, since it is the change in specific enthalpy h and not the absolute value that is important in practical problems. 1.7 Summary In thermodynamics, a working substance is any fluid (including gases) which receives, transports, and transfers energy in a system. The state or condition of a working substance at any location in any system may be determined if the thermodynamic properties of the substance at the location of interest are known.


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These properties include: • Pressure • Temperature • Density (and Specific Volume) • Internal Energy • Enthalpy • Entropy There are three basic phases in which a fluid may exist: solid, liquid, or gas. A fluid may exist in a combination of these phases such as a solid-liquid combination or a liquid-vapor (gaseous) combination; the state in which it exists is specified by its thermodynamic properties such as pressure, temperature, volume, etc. At least two properties of the fluid must be known in order to specify its state of existence.


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Definitions Pressure – force per unit area. Unit: lbf/ft2, lbf/in2, (P) Temperature – a measure of the average kinetic energy of the molecules of a substance. Unit: °F, °R, °C, °K (T) Density – mass of a substance per unit volume. Unit: lbm/ft3 (ρ) Specific Volume – volume occupied per unit mass of a substance. Unit: ft3/lbm (v) Internal Energy – motion energy stored in the individual molecules of a substance. Unit: BTU (U) Enthalpy – sum of the internal energy and flow energy of a substance. Unit: BTU (H) Entropy – an indication of the relative usefulness of energy. Unit: BTU/°R (S) Heat – energy in transition. Unit: BTU (Q) BTU – British thermal unit; amount of heat required to raise one pound mass of water 1°F Specific heat – heat required to raise the temperature of one pound mass of material by one degree. Unit: BTU/lbm°F (cp) Heat of fusion – heat required at melting temperature to change one pound mass of a solid into liquid form. Unit: BTU/lbm Heat of vaporization – heat required at vaporization temperature to change one pound mass of a liquid into gaseous form. Unit: BTU/lbm Fluid – any substance that conforms to the shape of its container. Steady flow system – a system in which all points remain in particular condition, and all energy transfers with surroundings occur at a steady rate. Process – the state path formed when the properties of a system change. Cycle – a series of processes which result in a final state of a system identical to the initial state of the system before the series of processes was begun. Sensible heat – the heat added to or removed from a substance to produce a change in its temperature.


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Latent heat – the amount of heat added to or removed from a substance to produce a change in phase (no temperature change occurs: isothermal). Open system – both energies and matter cross the boundaries. Closed system – energies may flow in or out, matter cannot cross the boundaries. Isothermal process – a constant-temperature process. Isobaric process – a constant-pressure process. Adiabatic process – a process in which no heat is transferred.


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EXERCISES


1.31

1.1.1 A liquid is considered to be saturated when:

A. It is at the boiling temperature and the addition of heat would cause vaporization B. Its temperature increases with an addition of heat C. It is converted to 100% vapor D. Its pressure is held constant with its temperature below the boiling point

1.1.2 Any vapor having a temperature above saturation temperature is a:

A. Saturated vapor B. Superheated vapor C. Dry saturated vapor D. Wet saturated vapor

1.1.3 The temperature of a subcooled liquid:

A. Is below the saturation temperature for a given pressure B. Is at the saturation temperature for a given pressure C. Will remain constant during heat addition or removal D. Is dependent upon the system pressure

1.1.4 A condition where the temperature of the liquid is below the boiling temperature for a given

pressure is the definition of a:

A. Saturated liquid B. Superheated liquid C. Subcooled liquid D. Boiling liquid

1.1.5 A liquid is considered to be subcooled when:

A. The temperature of the liquid is above the temperature at which the liquid will boil B. Heat addition results in an increase in the liquid temperature C. Heat addition results in no change in the liquid temperature D. The liquid starts to vaporize as heat is added

1.1.6 A liquid is considered to be a subcooled liquid when the liquid’s temperature:

A. Remains constant as heat is added B. Remains constant as heat is removed C. Is above the saturation temperature D. Is below the saturation temperature


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1.1.8 A plant electrician informs the Control Room that specific gravity on battery 1ED1 has

changed from 1.47 to 1.53. This means:

A. The density of the battery fluid has decreased. B. The mass of the battery fluid increased. C. The specific volume of the battery fluid has decreased. D. None of the above are true.

1.1.9 Which of the below best describes the term “specific volume”?

A. The amount of mass in a unit volume. B. The amount of space occupied by a single mass. C. The weight of a substance per unit mass. D. The amount of space occupied by a substance.

1.1.10 Select the best choice to complete the following:

Temperature change is not always a good measure of heat added to a fluid due to the concept of _______________________________.

A. Subcooling B. Saturation temperature C. Superheating D. Phase change

1.1.11 The component cooling water (CCW) fluid in a letdown heat exchanger removes heat at

23.2 BTU/lbm. CCW enters at 82°F and exits at 103°F. What is the specific heat of the cooling water?

A. 487.2 BTU - °F/lbm B. 1.1 BTU/lbm - °F C. 0.905 BTU - °F/lbm D. 23.2 BTU/lbm - °F


1-33

1.1.12 A measure of a molecule’s average kinetic energy is a definition of:

A. Heat B. Temperature C. Molecular kinetic energy (MKE) D. Entropy

1.1.13 The vapor phase of water has molecules with _______ Intermolecular forces and ________

Kinetic energy.

A. Small; small B. Small; large C. Large; infinite D. Large; small


The amount of heat which must be added to a liquid in order to convert all of the liquid to steam is called the ____________________________________________.

A. Latent heat of vaporization B. Latent heat of condensation C. Sublimation Temperature D. Superheat Temperature

1.1.15 The energy required to change one pound mass of saturated liquid to saturated steam is

called the __________________, and this required energy tends to ___________________ as the pressure of the working fluid increases.

A. Latent heat of fusion; remain the same B. Latent heat of vaporization; decrease C. Latent heat of fusion; increase D. Latent heat of vaporization; remain the same

1.1.16 If a liquid is saturated and pressure remains constant, the addition of heat will:

A. Raise the liquid to the boiling point B. Result in a subcooled liquid C. Result in a vaporization of the liquid D. Cause the liquid to become superheated


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1.1.18 Which of the following is NOT a characteristic of a saturated liquid?

A. The addition of heat will cause the liquid to boil with no temperature change. B. The liquid’s temperature depends on its pressure. C. The liquid’s temperature will increase as heat is added. D. The liquid is at a temperature at which boiling will occur.


A. Is below the saturation temperature for a given pressure. B. Is at the saturation temperature for a given pressure. C. Is constant during heat addition or removal. D. Is dependent upon the system pressure.

1.1.21 The plant is shutdown with the pressurizer in a saturated condition as follows:

Pressurizer liquid temperature = 588°F Pressurizer vapor temperature = 588°F Pressurizer pressure = 1410 psia

Pressurizer spray is initiated to lower pressurizer pressure to 1350 psia. When pressurizer pressure stabilizes at 1350 psia, liquid temperature will be _______________________ and vapor temperature will be _____________________.

A. The same; the same B. The same; lower C. Lower; the same D. Lower; lower

1.2.1 Select the best choice to answer the following:

Feedwater entering a steam generator is 440°F

Its temperature is ________°Kelvin, ________°Celcius and ________°Rankine.

A. 227; 500; 900 B. 900; 227; 500 C. 500; 227; 900 D. 227; 900; 500


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1.3.1 Which of the following will have a constant heat transfer rate?

A. Rectangular slab of a pure substance B. Rectangular slab of a composite substance C. Cylindrical body of a pure substance D. Cylindrical body of a composite substance

1.3.2 Cooling water enters a heat exchanger at 75°F and exits at 105°F, If the flow rate is 150

lbm/hr, what is the rate of heat removal? (Assume cp =

A. 4,950 BTU/hr B. 4,091 BTU/hr C. 4,500 BTU/hr D. 13,500 BTU/hr

1.5.1 The difference between the liquid temperature and the saturation temperature is the

definition of:

A. CHF (critical heat flux) B. DNBR (departure from nucleate boiling ratio) C. SCM (subcooling margin) D. DNB (departure from nucleate boiling)

1.6.1 The total amount of energy contained in a closed system is best described as its:

A. Potential energy plus kinetic energy plus flow energy B. Kinetic energy plus potential energy minus internal energy C. Potential energy plus kinetic energy minus flow energy D. Kinetic energy plus potential energy plus internal energy

1.7.1 Liquid that exists at the boiling point is said to be:

A. Subcooled B. Saturated C. Compressed D. Superheated

1.7.2 Which of the following best defines the temperature of a saturated liquid as related to

boiling point?

A. Below the boiling point B. At the boiling point C. Above the boiling point D. Unrelated to the boiling point


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A. Raise the liquid to the boiling point B. Result in a subcooled liquid C. Result in vaporization of the liquid D. Cause the liquid to become superheated

1.7.4 The pressurizer is solid at 2285 psig and 656°F. How much energy is required to vaporize

one lbm of water? Assume pressure remains constant.

A. 90.1 BTU B. 406 BTU C. 796.1 BTU D. 550.6 BTU

1.7.5 Which statement best describes the condensing process?

A. Rejection of latent heat of vaporization B. Addition of latent heat of fusion C. Sublimation of the steam in the condenser D. Is entropic expansion through the condenser


A. The temperature of the liquid is above the temperature at which the liquid will boil. B. Heat addition results in an increase in the liquid temperature. C. Heat addition results in no change in the liquid temperature. D. The liquid starts to vaporize as heat is added.


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1.1.1 A liquid is considered to be saturated when:

A. It is at the boiling temperature and the addition of heat would cause vaporization

B. Its temperature increases with an addition of heat C. It is converted to 100% vapor D. Its pressure is held constant with its temperature below the boiling point

1.1.2 Any vapor having a temperature above saturation temperature is a:

A. Saturated vapor B. Superheated vapor C. Dry saturated vapor D. Wet saturated vapor


A. Is below the saturation temperature for a given pressure B. Is at the saturation temperature for a given pressure C. Will remain constant during heat addition or removal D. Is dependent upon the system pressure

1.1.4 A condition where the temperature of the liquid is below the boiling temperature for a given

pressure is the definition of a:

A. Saturated liquid B. Superheated liquid C. Subcooled liquid D. Boiling liquid


A. The temperature of the liquid is above the temperature at which the liquid will boil B. Heat addition results in an increase in the liquid temperature C. Heat addition results in no change in the liquid temperature D. The liquid starts to vaporize as heat is added

1.1.6 A liquid is considered to be a subcooled liquid when the liquid’s temperature:

A. Remains constant as heat is added B. Remains constant as heat is removed C. Is above the saturation temperature D. Is below the saturation temperature


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1.1.7 Which statement best describes the relationship between a subcooled liquid and a

compressed liquid?

A. A compressed liquid has a higher pressure for a given temperature than does a subcooled liquid.

B. There is no difference between a compressed liquid and a subcooled liquid. C. A subcooled liquid is cooler than a compressed liquid. D. A compressed liquid has the same pressure but a lower temperature than a subcooled

liquid. 1.1.8 A plant electrician informs the Control Room that specific gravity on battery 1ED1 has

changed from 1.47 to 1.53. This means:

A. The density of the battery fluid has decreased. B. The mass of the battery fluid increased. C. The specific volume of the battery fluid has decreased. D. None of the above are true.

1.1.9 Which of the below best describes the term “specific volume”?

A. The amount of mass in a unit volume. B. The amount of space occupied by a single mass. C. The weight of a substance per unit mass. D. The amount of space occupied by a substance.


Temperature change is not always a good measure of heat added to a fluid due to the concept of _______________________________.

A. Subcooling B. Saturation temperature C. Superheating D. Phase change

1.1.11 The component cooling water (CCW) fluid in a letdown heat exchanger removes heat at

23.2 BTU/lbm. CCW enters at 82°F and exits at 103°F. What is the specific heat of the cooling water?

A. 487.2 BTU - °F/lbm B. 1.1 BTU/lbm - °F C. 0.905 BTU - °F/lbm D. 23.2 BTU/lbm - °F


1-39

1.1.12 A measure of a molecule’s average kinetic energy is a definition of:

A. Heat B. Temperature C. Molecular kinetic energy (MKE) D. Entropy

1.1.13 The vapor phase of water has molecules with _______ Intermolecular forces and ________

Kinetic energy.

A. Small; small B. Small; large C. Large; infinite D. Large; small


The amount of heat which must be added to a liquid in order to convert all of the liquid to steam is called the ____________________________________________.

A. Latent heat of vaporization B. Latent heat of condensation C. Sublimation Temperature D. Superheat Temperature

1.1.15 The energy required to change one pound mass of saturated liquid to saturated steam is

called the __________________, and this required energy tends to ___________________ as the pressure of the working fluid increases.

A. Latent heat of fusion; remain the same B. Latent heat of vaporization; decrease C. Latent heat of fusion; increase D. Latent heat of vaporization; remain the same


A. Raise the liquid to the boiling point B. Result in a subcooled liquid C. Result in a vaporization of the liquid D. Cause the liquid to become superheated


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1.1.18 Which of the following is NOT a characteristic of a saturated liquid?

A. The addition of heat will cause the liquid to boil with no temperature change. B. The liquid’s temperature depends on its pressure. C. The liquid’s temperature will increase as heat is added. D. The liquid is at a temperature at which boiling will occur.


A. Is below the saturation temperature for a given pressure. B. Is at the saturation temperature for a given pressure. C. Is constant during heat addition or removal. D. Is dependent upon the system pressure.

1.1.21 The plant is shutdown with the pressurizer in a saturated condition as follows:

Pressurizer liquid temperature = 588°F Pressurizer vapor temperature = 588°F Pressurizer pressure = 1410 psia

Pressurizer spray is initiated to lower pressurizer pressure to 1350 psia. When pressurizer pressure stabilizes at 1350 psia, liquid temperature will be _______________________ and vapor temperature will be _____________________.

A. The same; the same B. The same; lower C. Lower; the same D. Lower; lower

1.2.1 Select the best choice to answer the following:

Feedwater entering a steam generator is 440°F

Its temperature is ________°Kelvin, ________°Celcius and ________°Rankine.

A. 227; 500; 900 B. 900; 227; 500 C. 500; 227; 900 D. 227; 900; 500


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1.3.1 Which of the following will have a constant heat transfer rate?

A. Rectangular slab of a pure substance B. Rectangular slab of a composite substance C. Cylindrical body of a pure substance D. Cylindrical body of a composite substance

1.3.2 Cooling water enters a heat exchanger at 75°F and exits at 105°F, If the flow rate is 150

lbm/hr, what is the rate of heat removal? (Assume cp =

A. 4,950 BTU/hr B. 4,091 BTU/hr C. 4,500 BTU/hr D. 13,500 BTU/hr

1.5.1 The difference between the liquid temperature and the saturation temperature is the

definition of:

A. CHF (critical heat flux) B. DNBR (departure from nucleate boiling ratio) C. SCM (subcooling margin) D. DNB (departure from nucleate boiling)

1.6.1 The total amount of energy contained in a closed system is best described as its:

A. Potential energy plus kinetic energy plus flow energy B. Kinetic energy plus potential energy minus internal energy C. Potential energy plus kinetic energy minus flow energy D. Kinetic energy plus potential energy plus internal energy

1.7.1 Liquid that exists at the boiling point is said to be:

A. Subcooled B. Saturated C. Compressed D. Superheated

1.7.2 Which of the following best defines the temperature of a saturated liquid as related to

boiling point?

A. Below the boiling point B. At the boiling point C. Above the boiling point D. Unrelated to the boiling point


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A. Raise the liquid to the boiling point B. Result in a subcooled liquid C. Result in vaporization of the liquid D. Cause the liquid to become superheated

1.7.4 The pressurizer is solid at 2285 psig and 656°F. How much energy is required to vaporize

one lbm of water? Assume pressure remains constant.

A. 90.1 BTU B. 406 BTU C. 796.1 BTU D. 550.6 BTU

1.7.5 Which statement best describes the condensing process?

A. Rejection of latent heat of vaporization B. Addition of latent heat of fusion C. Sublimation of the steam in the condenser D. Is entropic expansion through the condenser


A. The temperature of the liquid is above the temperature at which the liquid will boil. B. Heat addition results in an increase in the liquid temperature. C. Heat addition results in no change in the liquid temperature. D. The liquid starts to vaporize as heat is added.

thermal science - chapter 1 - tarleton.edu least two properties of the fluid must be known in order...

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