Chap1_Notes_14F_ME311_PJF

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Chapter 1 - Introduction Cengel Florio 14F Nomenclature( SI Units) A area (m 2 ) C P specific heat at constant pressure (kJ/(kg-K)) C V specific heat at constant volume (kJ/(kg-K)) COP coefficient of performance d exact differential E stored energy (kJ) e stored energy per unit mass (kJ/kg) F force (N) g acceleration of gravity ( 9.807 m/s 2 ) H enthalpy (H= U + PV) (kJ) h specific enthalpy (h= u + Pv) (kJ/kg) h depth (m) h convective heat transfer coefficient (W/(m 2 -K) K Kelvin degrees k specific heat ratio, C P /C V k kilo or 10 3 k t thermal conductivity (W/(m-C)) MW molecular weight or molar mass (kg/kmol) M mega or 10 6 m mass (kg) N kg moles (kmol) n polytropic exponent (isentropic process, ideal gas n = k) isentropic efficiency for turbines, compressors, nozzles th thermal efficiency (net work done/ heat added) P pressure (kPa, MPa, psia, psig) Pa Pascal (N/m 2 ) , Exergy (kJ) Q net net heat transfer (Q in - Q out ) (kJ) q net Q net /m, net heat transfer per unit mass (kJ/kg) R particular gas constant (kJ/(kg K)) or R u /MW R u universal gas constant (= 8.3145 kJ/(kmol K) ) S entropy (kJ/K) s specific entropy (kJ/(kg K)) T temperature ( C, K, F, R) U internal energy (kJ) u specific internal energy (kJ/(kg K))

description

Thermodynamics Chapter 1 Lecture Notes

Transcript of Chap1_Notes_14F_ME311_PJF

  • Chapter 1 - Introduction Cengel

    Florio

    14F

    Nomenclature( SI Units)

    A area (m2)

    CP specific heat at constant pressure (kJ/(kg-K))

    CV specific heat at constant volume (kJ/(kg-K))

    COP coefficient of performance

    d exact differential

    E stored energy (kJ)

    e stored energy per unit mass (kJ/kg)

    F force (N)

    g acceleration of gravity ( 9.807 m/s2)

    H enthalpy (H= U + PV) (kJ)

    h specific enthalpy (h= u + Pv) (kJ/kg)

    h depth (m)

    h convective heat transfer coefficient (W/(m2-K)

    K Kelvin degrees

    k specific heat ratio, CP/CV

    k kilo or 103

    kt thermal conductivity (W/(m-C)) MW molecular weight or molar mass (kg/kmol)

    M mega or 106

    m mass (kg)

    N kg moles (kmol)

    n polytropic exponent (isentropic process, ideal gas n = k)

    isentropic efficiency for turbines, compressors, nozzles

    th thermal efficiency (net work done/ heat added) P pressure (kPa, MPa, psia, psig)

    Pa Pascal (N/m2)

    , Exergy (kJ)

    Qnet net heat transfer (Qin - Qout) (kJ) qnet Qnet /m, net heat transfer per unit mass (kJ/kg)

    R particular gas constant (kJ/(kg K)) or Ru /MW

    Ru universal gas constant (= 8.3145 kJ/(kmol K) )

    S entropy (kJ/K)

    s specific entropy (kJ/(kg K))

    T temperature ( C, K, F, R) U internal energy (kJ)

    u specific internal energy (kJ/(kg K))

  • Vol volume (m3 )

    Vol volume flow rate (m3/s)

    V velocity (m/s)

    v specific volume (m3/kg)

    v molar specific volume (m3/kmol)

    X distance (m)

    X exergy (kJ)

    x specific exergy (kJ/kg)

    x quality

    Z elevation (m)

    Nomenclature (continued)

    Wnet net work done [(Wout - Win)other + Wb] (kJ)

    where Wb = 2

    1PdV for closed systems and 0 for control volumes

    wnet Wnet /m, net work done per unit mass (kJ/kg)

    Wt weight (N)

    inexact differential, small amount of

    regenerator effectiveness

    relative humidity

    nonflow specific exergy (kJ/kg) flow exergy (kJ/kg)

    density (kg/m3)

    humidity ratio change of a property

    Subscripts, superscripts

    a actual

    bdy, b boundary

    f saturated liquid state

    g saturated vapor state

    fg saturated vapor value minus saturated liquid value

    gen generation

    H high temperature

    HP heat pump

    L low temperature

    net net heat added to system or net work done by system

    other work done by shaft and electrical means

    P constant pressure

    REF refrigerator

    rev reversible

    s isentropic or constant entropy or reversible, adiabatic

    sat saturation value

  • Vol constant volume

    1 initial state

    2 finial state

    i inlet state

    e exit state

    rates of transfer or per unit time

  • Chapter 1 - Introduction

    Cengel

    Florio

    14F

    INTRODUCTION Classical Thermodynamics

    Macroscopic description -average effect of large sample

    of molecules- for the interaction

    Newton's 3 laws for Newtonian mechanics. Describe an object!

    Define a force as a push or pull interaction between two material objects.

    A 1st law An object in motion remains in motion, an object at rest

    remains at rest unless acted upon by a net external force.

    B 2nd. The net external force acting on an object results in an acceleration

    of that object or a time rate of change of its linear momentum ( mass * velocity vector)

    of that object. F(net)=d(mV/gc )/ dt or

    C Conservation of linear momentum

    The rates of transfer of linear momentum to an object(F) = the time rate of change of

    linear momentum of the object.

    D 3rd For every action on an object, there is an equal( in magnitude) and opposite

    (in direction) reaction by the object

    /DE Dt Q W

    The study of thermodynamics is concerned with the ways energy is stored within a body

    and how energy transformations and transfers which involve heat and work, may take

    place. One of the most fundamental laws of nature is the conservation of energy

    principle. It simply states that during an energy interaction, energy can change from one

    form to another but the total amount of energy remains constant. That is, energy cannot

    be created or destroyed. SANKEY

    Classical thermodynamics ( model matter as continuous) is based on the macroscopic

    approach where a large number of particles, [1 kgmole contains 6.023x1026

    particles ]

    molecules, makes up the substance in question. The macroscopic approach to

    thermodynamics does not require knowledge of the behavior of individual particles and

    is called classical thermodynamics. It provides a direct and easy way to obtain the

    solution of engineering problems without being overly cumbersome. A more elaborate

    approach, based on the average behavior of large groups of individual particles, is called

    statistical thermodynamics. This microscopic approach is rather involved and is not

  • reviewed here and leads to the definition of the second law of thermodynamics. We will

    approach the second law of thermodynamics from the classical point of view and will

    learn that the second law of thermodynamics asserts that energy has quality as well as

    quantity, and actual processes occur in the direction of decreasing quality of energy.

    Let represent volume

    Properties in Classical thermodynamics

    29

    0

    limm

    Den

    sity

    ,

    Molecular and atomic

    effects are important-(mfpl-e-8m)

    Limit of the macroscopic

    model and assumptions. Vol of

    Continuum point

    (m3)0

  • Engineering-Application Areas of Thermodynamics

    13

    Gas turbine

    14

  • Systems Example-open-Eulerian

    15

    Example of a System-C &O-Deforming boundary(slide 4)

    16

    Boundary

    of fms

    Closed, Open, and Isolated Systems

    Thermodynamic system, or simply system, is defined as a quantity of matter or a

    region in space set aside for study. The region outside the system is called the

    surroundings or environment of the system. The real or imaginary mathematical

    carsmokecombo.mov

  • surface that separates the system from its surroundings is called the boundary. The

    boundary of a system may be fixed or movable.

    Surroundings are physical space outside the system boundary.

    Systems may be considered to be closed or open, depending on whether a fixed mass or

    a fixed volume in space is chosen for study.

    \\

  • For the time under study, A closed system consists of a fixed amount of macroscopic

    mass and no mass may cross the system boundary. The closed system is identified by its

    boundary, which is a mathematical surface having no mass or thickness, this boundary

    may move and change shape (deform).

    Examples of closed systems are sealed tanks and piston cylinder devices (note the

    volume does not have to be fixed). However, energy in the form of heat and work may

    cross the boundaries of a closed system.

  • An open system, or control volume, has mass as well as energy crossing the boundary,

    called a control surface. Examples of open systems are pumps, compressors, turbines,

    valves, nozzles, and heat exchangers. Car Radiator

    A system defined such that no interactions occur , i.e. no heat, work, or mass transfers is

    called an isolated system.

    An isolated system is a general system of fixed mass where no heat or work may cross

    the boundaries. An isolated system is a closed system with no energy crossing the

    boundaries and is normally a collection of a main system and its entire surroundings that

    are exchanging mass and energy among themselves and no other system.

    Isolated System Boundary

    Although the principles are the same,the forms of the thermodynamic relations that

    are applicable to closed and open systems are different, it is extremely important

    that we recognize the type of system we have before we start analyzing it.

    Energy , an extensive property (Characteristic)

    Consider the system shown below with the center of mass moving with a velocity, V ,

    relative to a reference, at an elevation, Z, relative to the reference plane.

    Isolated System Boundary

    Mass

    System

    Surr 2

    Surr 3

    Surr 4

    Mass

    Heat

    Work

    Surr 1

    Heat = 0

    Work = 0

    Mass = 0

    Across

    Isolated

    Boundary

    Z

    General

    System

    CM

    Arbitrary Reference Plane Z=0

    V

  • Energy-E= U +KE +PE

    The total energy, E, of a system is the sum of all forms of energy that can exist within

    the system such as thermal, mechanical, chemical and nuclear, kinetic, potential,

    electric and magnetic. The total energy of the system is the sum of the internal energy,

    macroscopic kinetic energy, and potential energy. The internal energy, intrinsic ,U, is

    that energy associated with the internal molecular structure of a system and the

    degree of the molecular activity . The macroscopic kinetic energy, KE, extrinsic,

    exists as a result of the system's motion relative to an external reference frame. When

    the system moves with velocity, V , the kinetic energy is expressed as

    2

    ( )2

    VKE m kJ

    The macroscopic energy that a system possesses as a result of its elevation in a

    gravitational field relative to the external reference frame is called potential energy, PE,

    and is expressed as

    ( )KE mgZ kJ

    where g is the gravitational acceleration and z is the elevation of the center of mass of a

    system relative to the reference frame. The total energy of the system is expressed as

    ( )E U KE PE kJ

    or, on a unit mass basis, or specific,

    2

    (

    2

    )E U KE PE k

    V gZu

    Je

    m m m m g

    J J

    k

    where e = E/m is the specific stored energy, and u = U/m is the specific internal energy

    ,depends on the internal structure. The change in stored energy of a system due to a

    change in state is given by

    ( )E U KE PE kJ

    Most closed systems remain stationary during a process and, thus, experience no change

    in their kinetic and potential energies. The change in the stored energy is identical to the

    change in internal energy for stationary systems.

  • If KE = PE = 0,

    ( )E U kJ

    Property: Any instantaneously measureable ( directly or indirectly) characteristic of a system in

    equilibrium is called a property.

    The value of a property is independent of the path used to arrive at the system

    condition.

    Some thermodynamic properties are pressure P, temperature T, volume V, and mass m.

    Properties may be intensive or extensive.

    Extensive properties are those that vary directly with size---or extent---of the system and

    are mass dependent properties.

    Some Extensive Properties( can subdivide)

    a. mass

    b. volume

    c. total energy

    d. mass dependent property, S, H,

    Intensive properties are those that are independent of size or quantity of mass.

    Some Intensive Properties(cannot subdivide)

    a. temperature

    b. pressure

    d. color

    e. any mass independent property

  • For equilibrium states, extensive properties per unit mass are intensive properties. For

    example the specific volume v defined as

    3Volume V m

    vmass m kg

    and density defined as

    3

    mass m kg

    volume V m

    are intensive properties.

    5

    Equilibrium requires uniformity of all intensive properties, so if isolated the system experiences no change of state.

    Theoretically over a finite period of time equilibrium- requires isolation because any interchange will result in a change in a characteristic- i.e. property or change with position within.

    If change is slow enough compared to the time to obtain uniformity called quasi-equilibrium.

    Classification of equilibrium Properties

    Intensive properties- Properties independent of size or mass of system, P T

    Extensive- Dependent on the size or quantity of mass Vol, Mass, Energy ,upper case symbol

    For homogeneous system, intensive can be formed by the ratio of two extensive

    ,if mass-specific properties are lower cased

    Extrinsic Properties are those that are independent of the internal structure of the substance; Kinetic energy, location in fields

    Intrinsic Properties are those that are dependent on the internal structure of the matter, P, T, U

    STATE- condition of the system identified by means of all relevant properties of the system. Minimum set sufficient to determine all other properties.

    A simple substance is a pure substance with one reversible work mode.

    Dimensions & Units

    Dimensions are qualitative description of a physical quantity.

    Units are quantitative descriptions.

    In science, we require that all equations in symbolic form must be dimensionally

    homogeneous.

    An important component to the solution to any engineering thermodynamic problem

    requires the proper use of units and dimensions. The dimensional as well as unit checks

    are the simplest of all engineering checks that can be made for a given solution. Use of

    inconsistent units present a major hindrance to the correct solution of thermodynamic

    problems, learn to use units carefully and properly. The system of units selected for this

  • course is the SI System that is also known as the International System (sometimes called

    the metric system). In SI, the basic dimensions are mass, length, and time and units are

    the kilogram (kg), meter (m), and second (s), respectively. We consider force to be a

    derived dimension from Newton's second law, i.e.,

    ( )( )Force mass acceleration

    F ma

    [F}={m}[L}/[t]2

    NUMBERS HAVE UNITS, SYMBOLS HAVE DIMENSIONS

    In SI, the force unit (measure) is the Newton (N), and it is defined as the force required

    to accelerate a mass of 1 kg at a rate of 1 m/s2. That is,

    21 (1 )(1 )

    mN kg

    s

    The term weight is often misused to express mass. Unlike mass, weight Wt is a force.

    Weight is the gravitational force applied to a body, and its magnitude is determined from

    Newton's second law.

    = tWt mg

    where m is the mass of the body and g is the local gravitational acceleration (g is 9.807

    m/s2 at sea level and 45 latitude). The weight of a unit volume of a substance is called

    the specific weight w and is determined from w = g, where is density.

    IMPORTANCE OF DIMENSIONS AND UNITS Any physical quantity can be characterized by

    dimensions. A Qualitative description, i.e. work, mass, acceleration, velocity, position, etc.

    Units-The standards of measures so that numerical values can be assigned physical quantities or associated with the dimensions -A Quantitative measure

    Some basic dimensions such as mass m, length L, time t, and temperature T are selected as primary or fundamental dimensions, while others such as velocity V, energy E, and volume V are expressed in terms of the primary dimensions and are called secondary dimensions, or derived dimensions. We will treat Force as a derived Dimension

    Metric SI system: A simple and logical system based on a decimal relationship between the various units.[ M,L,t]

    English system: It has no apparent systematic numerical base, and various units in this system are related to each other rather arbitrarily.[ Various choices, if use M.L.t] Slide 52

    19

  • Often times, the engineer must work in other systems of units. Comparison of the

    United States Customary Units (USCS), or English, and the slug systems of units with

    the SI system is shown below.

    Dimensions SI USCS Slug

    mass kilogram (kg) pound-mass (lbm) slug-mass (slug)

    time second (s) second (s) second (s)

    length meter (m) foot (ft) foot (ft)

    force Newton (N) pound-force (lbf) pound-force (lbf)

    [m]=[F][t]2 /[L]

    Sometimes we use the mole number as a measure of the mass. In the SI units the mole

    number is in kilogram-moles, or kmol, a quantity of mass that is numerically equal to its

    molecular mass.

    Newtons second law is often written in a more general form as

    = c

    maF

    g

    where gc is called the gravitational constant and is obtained from the force definition. In

    the SI System 1 Newton is that force required to accelerate 1 kg mass 1 m/s2. The

    gravitational constant in the SI System is

    2

    2

    (1 )(1 )

    = 11

    c

    mkg

    ma kg msgF N N s

    In the USCS 1 pound-force is that force required to accelerate 1 pound-mass 32.176 ft/s2.

    The gravitational constant in the USCS is

    2

    2

    (1 )(32.2 )

    = 32.21

    c

    ftlbm

    ma lbm ftsgF lbf lbf s

    In the slug system, the gravitational constant is

    2

    2

    (1 )(1 )

    = 32.174 or 1 slug =32.174lb1

    c m

    ftslug

    ma lbm ftsgF lbf lbf s

    Example 1-1

    An object at sea level has a mass of 400 kg.

    a) Find the weight of this object on earth.

    b) Find the weight of this object on the moon where the local gravitational

    acceleration is one-sixth that of earth.

    (a)

  • tWT mg

    2

    2

    1 (400 )(9.807 )( )

    3922.8

    t

    m NW kg

    mskg

    s

    N

    (b)

    2

    2

    /6

    9.807 1(400 )( )( )

    6

    653.8

    t earthW mg mg

    m Nkg

    mskg

    s

    N

  • Example 1-2E

    An object has a mass of 180 lbm. Find the weight of this object at a location where the

    local gravitational acceleration is 30 ft/s2. Express the weight in lbf

    2

    2

    /g

    1(180 )(30 )( )

    32.2

    167.7

    t cW mg

    ft lbflbm

    ftslbm

    s

    lbf

    State, Equilibrium, Process, and Properties

    State

    Condition of the system identified by the values of its properties.

    Consider a system in complete balance such that if isolated it does not undergoing any change. The properties can be measured or calculated throughout the

    entire system. This gives us a set of properties that completely describe the condition or

    state of the system. At a given state all of the properties are known; changing one

    property changes the state.

    Equilibrium- No unbalanced Potentials

    A system is said to be in thermodynamic equilibrium if isolated (no possible

    interaction)it maintains thermal (uniform temperature), mechanical (balanced forces),

    phase (the mass of two phases, e.g. ice and liquid water, in equilibrium) and chemical

    equilibrium.

    Process Any change from one state to another is called a process (Thus at least one property

    changes during the process). During a quasi-equilibrium or quasi-static process the

    Equilibrium=2nd Law

    If isolated, a system

    always proceeds from a

    macroscopic state of

    relative disorder to a

    state of relative order.

    non-

    equilibrium

  • system remains practically infinitesimally close to equilibrium at all times. We study

    quasi-equilibrium processes because they are easy to analyze (equations of state apply)

    and work-producing devices deliver the most work when they operate on the quasi-

    equilibrium process. (the time required to achieve equilibrium is much smaller than the

    process time, therefore engineering wise we can assume a continuous series of

    equilibrium states exist, path exists.

    In some common thermodynamic processes are those where one thermodynamic

    property is held constant. Some of these common processes are:

    Process Property held constant

    isobaric pressure

    isothermal temperature

    isochoric volume

    isentropic entropy (see Chapter 6)

    Free body diagram

    We can understand the concept of a constant pressure process by considering the above

    figure. The force exerted by the water on the face of the piston has to equal the force

    due to the combined weights of the piston and the bricks and atmos pressure . If the

    combined weight of the piston and bricks is constant then F is constant and the pressure

    at continuum points are constant even when the water is heated.

    We often show the process on a P-V diagram as shown below.

    Constant Pressure Process

    Water

    F

    System

    Boundary

  • State Postulate

    As noted earlier, the state of a system is described by its properties. But by

    experience not all properties must be known before the state is specified. Once a

    sufficient number of properties are known, the state is specified and all other properties

    are known. The number of properties required to fix the intensive state of a simple,

    homogeneous system is given by the state postulate:

    A simple system is one in which the effects of motion, viscosity, fluid shear,

    capillarity, an-isotropic stress and external force fields are absent. One reversible

    work mode

    The equilibrium thermodynamic state ,intrinsic equilibrium

    state, of a simple compressible system is completely specified by

    two independent intensive properties.

    Compressible implies that for a fms of the substance, the only

    reversible work is boundary work or PdVol.

    Cycle

    A process (or a series of connected processes) with identical end states, initial and

    final, is called a cycle. Below is a cycle composed of two processes, A and B. Along

    process A, the pressure and volume change from state 1 to state 2. Then to complete the

    cycle, the pressure and volume change from state 2 back to the initial state 1 along

    process B. Keep in mind that all other thermodynamic properties must also change so

    that the pressure is functions of volume as described by these two processes.

    Process

    B

    Process

    A

    1

    2 P

    V

  • Pressure

    Force per unit area is called pressure, and its unit is the Pascal, N/m2 in the SI system

    and psia, lbf/in2 absolute or psia, in the English system. A fluid can only experience a

    compressive stress, i.e. into the surface.

    Force FP

    Area A

    3

    2

    6 3

    2

    1 10

    1 10 10

    NkPa

    m

    NMPa kPa

    m

    1 bar= 100 kPa

    The pressure used in all calculations of state is the absolute pressure measured relative

    to absolute zero pressure. However, pressures are often measured relative to

    atmospheric pressure called gage or vacuum pressures. In the English system the

    absolute pressure and gage pressures are distinguished by their units, psia (pounds

    force per square inch absolute) and psig or psi (pounds force per square inch gage),

    respectively; however, the SI system makes no distinction between the units of

    absolute and gage pressures.

    These pressures are related by[ Feq=PA- Patm A; F into wall; - Feq= Patm A- PA;

    -Feq away from wall]

    : When the Absolute pressure is greater than that of the surroundings-atmgage abs atmP P P

    Absolute pressure is below that of the surroundings-atm ; When the vac atm absP P P

  • Or, these last two results may be written as with negative gage = vacuum

    | |abs atm gageP P P

    Where the +Pgage is used when Pabs > Patm and Pgage is used for a vacuum gage.

    The relation among atmospheric, gage, and vacuum pressures is shown below.

    Small to moderate pressure differences are measured by a manometer and a differential

    fluid column of height h corresponds to a pressure difference between two points in the

    system a continuous fixed composition fluid in equilibrium

    / ; as wellas dP/dx=0 and dP/dy=0

    is called the specific weight or weight/volume

    In a continuous fluid , density is a c

    For

    dP dz g g

    ontinuous funtion of position

    surfaces of constant pressure are horizontal s

    liquids ; Bulk modulius of comp

    urface

    ressib

    s.

    ilit

    This pressure difference is determined from fluid displaced height as

    for 8) 1/In addition for a series of fluid in equilibrium, the equilibrium position is layered

    Pressure is continuous across the boundaries, but the variation is n

    y 1

    ot .

    / / 1

    an inco

    0

    mpress

    TkPa

    Fo

    d dP v O

    r

    v

    2 1

    ible substance , the pressure change across an depth of h is

    ;a linear relation, ( ) where h is the relative depth of

    location 2 relative to location 1 in a continuous fluid

    P P P g h kPa

  • Pressure measuring devices use - Change cross-sectional

    shape or uncoiling of sample tube

    HW 1-

    Prob 8 3.28 kN

    Prob 18 Cm V2 /t

    Prob 79 8.34 kPa

    Prob 83 0.582 m

    Prob 125 FD = Cdrag Afrontal V2

    Example 1-3

  • A vacuum gage connected to a tank reads 30 kPa (thus vacuum)at a location where the

    atmospheric pressure is 98 kPa. What is the absolute pressure in the tank?

    The vacuum gage measures an absolute pressure which is less than atmospheric and

    reports that difference

    98 30

    68

    vac atm abs

    abs atm vac

    P P P

    P P P

    kPa kPa

    kPa

    Example 1-4

    A pressure gage connected to a valve stem of a truck tire reads 240 kPa at a location

    where the atmospheric pressure is 100 kPa. What is the absolute pressure in the tire, in

    kPa and in psia? Since the pressure gage is measuring the difference between the

    atmospheric pressure and the pressure of the air in the tire,

    100 240

    340

    abs atm gageP P P

    kPa kPa

    kPa

    Notice units

    The pressure in psia is

    14.7340 49.3

    101.3abs

    psiaP kPa psia

    kPa

    Notice units and the difference

    What is the gage pressure of the air in the tire, in psig?

    49.3 14.7

    34.6

    gage abs atmP P P

    psia psia

    psig

    Check the tire side walls on your car or truck. What is the maximum allowed pressure?

    Is this pressure in gage or absolute values?

  • Example 3

    48

    gh

    1-83 The gage pressure of air in a pressurized water tank is measured simultaneously by both a pressure

    gage and a manometer. The differential height h of the mercury column is to be determined.

    Assumptions The air pressure in the tank is uniform (i.e., its variation with elevation is negligible due to its

    low density), and thus the pressure at the air-water interface is the same as the indicated gage pressure.

    Properties We take the density of water to be w =1000 kg/m3. The specific gravities of oil and mercury are

    given to be 0.72 and 13.6, respectively.

    Analysis Starting with the pressure of air in the tank (point 1), and moving along the tube by adding (as we

    go down in a continuous fluid) or subtracting (as we go up in a continuous fluid ) the quantity

    term until we reach the free surface of oil where the oil tube is exposed to the

    atmosphere, and setting the result equal to the pressure there , Patm in Pascals gives

    1 w Hg Hg oil oil

    start end

    w atm

    P P P

    P gh gh gh P

    Rearranging,

    wghghghPP wHgHgoiloilatm1 or,

    whhhg

    P HgHgoiloil

    w

    gage,1SGSG

    Substituting,

    m 3.013.6m) (0.7572.0mkPa. 1

    m/skg 1000

    )m/s (9.81)kg/m (1000

    kPa 80Hg2

    2

    23

    h

    Solving for hHg gives hHg = 0.582 m. Therefore, the differential height of the mercury

    column must be 58.2 cm.

    Discussion Double instrumentation like this allows one to verify (calibrate) the

    measurement

    of one of the instruments by the measurement of another instrument.

  • Example 1-5

    Both a gage and a manometer are attached to a gas tank to measure its pressure. If the

    pressure gage reads 80 kPa, determine the distance between the two fluid levels of the

    manometer if the fluid is mercury whose density is 13,600 kg/m3

    one side being exposed

    to the gas and the other side exposed to the atmosphere. Sketch the system.

    3 3

    3 2 2

    10 /

    80

    113600 9.807

    /

    0.6

    N m

    kPa kPahkg m N

    m s kg m s

    m

    Temperature

    Although we are familiar with temperature as a measure of hotness or coldness, it is not easy to give an exact definition of it. However, temperature is considered as a

    thermodynamic property that is the measure of the energy content of a mass. When heat

    energy is transferred to a body, the body's energy content increases and so does its

    Notice the pressure difference

    not the absolute pressure

    Ph

    g

  • temperature. In fact it is the difference in temperature that causes energy transfer, called

    heat, to flow from a hot body to a cold body. Two bodies are in thermal equilibrium

    when they have reached the same temperature. It is observed that if two bodies are in

    thermal equilibrium with a common third body, they are also in thermal equilibrium with

    each other. This simple fact is known as the zeroth law of thermodynamics.

    The temperature scales used in the SI and the English systems today are the Celsius

    scale and Fahrenheit scale, respectively. These two linear scales are based on a

    specified number of degrees between the same states, the freezing point of water ( 0 C

    or 32 F) and the boiling point of water (100 C or 212 F) and are related by

    [ 32] [ 0]

    [212 32] [100 0]

    [ 32]5 / 9

    459.6

    273.15

    9

    7

    * / 5

    F F

    F C

    R F

    K C

    k C

    R F

    F C

    T T

    T T

    T T

    T T

    T T

    T T

    T T

  • Example 1-6

    Water at one atmosphere pressure boils at temperature of 212 F. At what temperature

    does water boil (change phase) in C.

    5 5T = ( 32) (212 32) 100

    9 9C F

    CT F C

    F

    Like pressure, the temperature used in thermodynamic calculations must be in

    absolute units. The absolute scale in the SI system is the Kelvin scale that is related to

    the Celsius scale by

    = C+ 273.15 T K T

    In the English system, the absolute temperature scale is the Rankine scale, which is

    related to the Fahrenheit scale by

    = F+ 459.67 T R T

  • The magnitudes of each division of 1 K and 1C are identical, and so too are the

    magnitudes of each division of 1 R and 1F. That is,

    2 1

    2 1

    = ( C + 273.15)- ( C + 273.15)

    = C - C

    = C

    T K T T

    T T

    T

    and

    F T R T

    5/9 R T K T

  • A It is to be shown that the power needed to accelerate a car is proportional to the mass and the square of

    the velocity of the car, and inversely proportional to the time interval.

    Assumptions The car is initially at rest.

    B

    Fresh

    Water

    hw

    hsea

    hoil

    Sea

    Water

    Mercury

    Oil

    hHg