FLIP THERMOFLUID

CHAPTER 1
INTRODUCTION TO THERMAL AND

FLUIDS ENGINEERING

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

CHAPTER 1 INTRODUCTION TO THERMAL AND FLUIDS
ENGINEERING

INTRODUCTION

Cars of the 21st century are dramatically improved over those of the early 1900s. The
advances in engineering are the result of improved technical knowledge and the
systematic application of this knowledge. The intelligent use of basic thermal and fluids
engineering principles has improved the design of cars and other thermal-fluids systems
as diverse as buildings and window air conditioners.

In thermal-fluids systems, the focus is on energy: its use, conversion, or transmission in
one form or another. To analyze these systems, one, two, or three energy disciplines are
needed, separately or in combination. These disciplines are:

a. Thermodynamics, the study of energy use and transformations from one form
to another and the physical properties of substances (solids, liquids, gases)
involved in energy use or transformation

b. Heat Transfer, the study of energy flow that is caused by a temperature
difference

c. Fluid mechanics, the study of fluids (liquids, gases) at rest or in motion and
the interactions between a solid and a fluid either flowing past or acting on the
solid in some method

Think to use the automobile to illustrate how these three subjects must be used
together and separately.

To begin an analysis, we must decide what aspect of the car we want to study. Is it the
engine, the radiator where heat is removed from the engine coolant and released into the
atmosphere, the water pump, the fuel supply system (pump, fuel lines, and fuel injector),
the air-conditioning system, or the passenger compartment?

Do we want to examine the water-cooling system to determine what is needed to pump
water through the engine-cooling system, the heat transfer from the water to the air
flowing through the radiator, the 'conversion of the chemical energy in the gasoline to
mechanical power in the engine, the energy contained within the exhaust gases, the
refrigerant flow in the air-conditioning system, or the air flow through the air-conditioning
system into the passenger compartment? Clearly, we need to identify carefully what we
want to study.

LEARNING OBJECTIVES

At the end of this chapter, you should be able to:

1. Describe the concepts involved in a thermal fluids system
2. Explain the three energy disciplines are Thermodynamics, Heat Transfer, and Fluid

Mechanics.

KKTM 1

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

1.1 THERMAL AND FLUIDS SYSTEMS

Figure 1.1: Schematic of engine water-cooling system

Let us consider several of these car systems or subsystems. The water-cooling
system (Figure 1.1) includes four main components:
1. A water pump,
2. The engine block,
3. The radiator, and
4. The radiator fan.

Pipes connect the first three components, and there are water passages inside the
engine block.

Thermodynamic analysis of the engine would tell us how much heat must be
removed from the engine block by the water and rejected by the water in the
radiator to the air flowing through the radiator.

Heat transfer analysis would tell us the number and size of passages needed in
the engine block to remove the heat and would permit us to determine the
necessary size of the radiator.

Fluid mechanics would help us determine the pressure that must be produced by
the water pump to overcome resistance to flow in the water passages, pipes, and
waterside of the radiator and by the fan to overcome the flow resistance on the
airside of the radiator. Fluid mechanics also would tell us the power required to
drive both the water pump and the fan.

Example
1.1:

Question:

What is the focus In thermal-fluids systems?

Solution:

The focus is on energy: its use, conversion, or transmission in one form or another.

KKTM 2

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

Example 1.2:
Question:
What is the difference between thermodynamic and fuild mechanics?
Solution:
Thermodynamics, the study of energy use and transformations from one form to
another and the physical properties of substances (solids, liquids, gases) involved
in energy use or transformation

Example 1.3:
Question:
List of four main components in water cooling system.
Solution:
1. Water pump
2. Engine Block
3. Radiator
4. Fan

EXERCISE 1.1

1. Explain the engineering analysis of water-cooling system in term of:
(a) Thermodynamics Analysis
(b) Heat Transfer Analysis
(b) Fluid Mechanic Analysis

2. List of typical thermal-fluid system in manufacturing
3. Explain the thermodynamics, heat transfer, and fluid mechanics of refrigeration

system.

KKTM 3

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

1.2 THERMODYNAMICS

Thermodynamics can be considered the unifying idea for the solution of thermal-
fluids system problems. The governing concepts are: conservation of mass,
conservation of energy (also called the first law of thermodynamics), and the
second law of thermodynamics.

Figure 1.2 A system interacting with the surroundings

Before we can discuss these concepts, we must set up a system and terminology
for approaching the subject logically. We begin with identifying what we want to
study.

The object we analyze is called a system (Figure 1.2). The region in space that
contains the system is called the control volume. Everything inside this line is the
system; everything outside this line is the surroundings. Our analysis is dictated by
the choice of the boundary, and several different boundaries might be chosen.

In thermodynamics, we can identify three types of systems.' A closed system
(Figure l.3a) is one in which no mass crosses the boundary. Energy in any form
can pass through the boundary.

For example, suppose we want to determine how long it would take to boil water in
a pan on a stove. We add a fixed mass of water to the pan and over it with a
perfectly sealing lid. (Ignore the air in the pan.) We identify the boundary as the
inside surface of the pan and lid, and the system is only the water. We now turn on
the stove.

Heat transfer from the gas flame raises the temperature of the water until it begins
to boil. Because of the lid, the amount of water (mass) in the system does not
change; it is the same mass as at the beginning of the heating. A slightly more
involved example could be a piston-cylinder assembly, similar to what is used in an
engine.

We assume there is perfect sealing between the piston and the cylinder and
between the inlet and exhaust valves and cylinder head, so that no gas can
escape from the assembly. We define the boundary to follow the walls of the
cylinder and the top of the piston, so that the system is only the gas contained in
the piston-cylinder assembly.

KKTM 4

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

Heat is added, and the piston moves because of the temperature increase in the
gas. In both of these examples, the mass of the system is fixed. The volume of the
first system (pot of water) is constant; the volume of the second system (piston-
cylinder assembly) changes. Heat crosses the boundary in both systems.

Figure 1.3 Examples of (a) a closed system and (b) an open system

In the second system, mechanical work also crosses the boundary. (From physics,
mechanical work, W, is defined as a force operating through a distance, and a
force operates on the piston-face force due to the pressure in the cylinder.) All this
information may be needed to analyze these two systems.
THINK: An open system is one in which both mass and energy can pass through the

boundary.
The various devices described above undergo some sort of process. The water in
the pan is heated. Power is extracted from the expanding air in the piston-cylinder
assembly. Heat is transferred from the electronic components in a computer to the
air flowing over them and is blown into the room surrounding the computer.

KKTM Figure 1.4 Two types of process: (a) steady, and (b) unsteady
5

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

A process occurs whenever some property of a system changes or if there is an
energy or mass flow across the boundary of the system. In the boiling water
example, the properties that change are the temperature of the water and the total
energy in the water. Because the properties of interest are different between the
start and finish of the process (at different times), this is called an unsteady (or
transient) process (Figure 1-4).

In the computer-cooling example, both mass and energy (heat and electrical work)
flow across the boundary. The property of interest may be the temperature of the
air. The air temperature changes with location (from inlet to exit) but does not vary
with time at either inlet or exit. This is called a steady process.

Example 1.4:

Question:

What is the control volume?

Solution:

The control volume is the region in space that contains the system.

Example 1.5:

Question:

What is the difference between close system and opensystem?

Solution:

A closed system is one in which no mass crosses the boundary. Energy in any
form can pass through the boundary, and an open system is one in which both
mass and energy can pass through the boundary.

KKTM 6

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

EXERCISE 1.2

1. For the following systems, define a control volume and state whether the system
is open or closed and steady or unsteady. Identify any and all heat transfer,
energy flows, mass flows, and energy transformations flows.
a. Rocket
b. Pot of boiling water with no lid

2. Define a control volume, state if the system is steady or unsteady, open or
closed, constant volume or changing volume, constant fluid density or changing
fluid density. Also, identify all heat transfer, energy flows, and mass flows.
a. Helium tank being filled
b. Helium balloon being filled

KKTM 7

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

1.3 HEAT TRANSFER

Heat is transferred wherever there is a temperature difference between two points
in a substance, whether that substance is a solid, liquid, gas, or plasma. Three
types of heat 'transfer can occur-conduction, convection, and radiation-but
regardless of the mode of heat transfer, a temperature difference drives the
process.

In the manufacturing of optical fibers, a long thin filament of glass is drawn
continuously from a high-temperature furnace. The molten glass must be cooled
before the fiber can be coated with a protective seal. This is accomplished by
blowing cold gas over the fiber.

In the winter, houses often have drafts of cold air along the floor. Heat transfer
from a warm house to the cold outside air causes a decrease in the air
temperature near the inside wall. Due to this cooling, the density of the air near the
wall increases, and buoyancy causes this air to flow downward. Hotter air from
near the ceiling replaces the cooled air, and a circulation cell is formed. This
moving air past the solid surface results in natural convection heat transfer (also
called free convection heat transfer). "Natural" means that buoyancy forces induce
flow.

Whereas convection and conduction require some sort of material for heat transfer
to occur, radiation heat transfer can occur in the presence of a vacuum or in the
presence of a transparent or semitransparent solid, liquid, gas, or plasma. A few
examples of radiation heat transfer are the greenhouse effect.

On a clear summer day, the interior of a car with all its windows closed will have a
much higher temperature than the outside air. Solar energy passes through the car
windows (Figure 1.5), is absorbed by the interior seats, and then is reemitted.
However, the reemitted energy cannot pass through the glass as easily as the
solar energy. Hence, the trapped energy raises the air temperature. This is called
the greenhouse effect.

KKTM Figure 1.5 The greenhouse effect causes high
temperatures inside the car

8

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

Example 1.6:
Question:
What is the heat transfer?
Solution:
Heat transfer is a condition whenever the temperature difference between two
points in a substance, whether that substance is a solid, liquid, gas, or plasma

Example 1.7:
Question:
List of three types of heat transfer?
Solution:
a. conduction,
b. convection, and
c. radiation

EXERCISE 1.3

1. Explain the heat transfer occurs on:
a. Conduction
b. Convection
c. Radiation

2. Explain the greenhouse effect.

KKTM 9

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

1.4 FLUID MECHANICS

Fluid mechanics is often divided into two general areas; one associated with fluids
at rest-hydrostatics-and the other addressing relative motion between a fluid and a
solid surface-fluid dynamics. In each case; we deal with a substance-a fluid that
will deform or change shape if a shear (or tangential) force is applied to it, no
matter how small this force is. A fluid will not necessarily deform if we apply a
normal force to it.

One way to visualize this is to consider a stack of 500 sheets of paper. If we push
down normally (perpendicularly) on the stack with our finger, nothing moves.
However, if we lay our hand on the stack of paper and push sideways (parallel to
the sheets), the sheets will slide over each other and the stack changes shape.

Hydrostatics (or fluid statics) deals with forces exerted by a stationary fluid on a
solid surface. A few examples follow:

(a) The Monterey Bay Aquarium is a 326,000-gallon tank in which hundreds of
fish from all over the world are displayed. To design the frames and support
structure around the viewing windows, and to help determine the required
window thickness, hydrostatics is used to calculate the forces on the window.
In another example, the forces exerted on a dam (Figure 1.6) must be
calculated so that the strength required holding back the reservoir is
engineered into the dam.

(b) Many systems have internal pressures different from that outside. Examples
include aircraft flying at high altitudes, spacecraft, submarines, pipelines,
helium tanks, and so on. Forces acting on the surfaces separating the two
pressures can be calculated using hydrostatic principles.

(c) Hydraulic systems used in car and aircraft brakes, car hoists, and other
hydraulic

Figure 1.6 Schematic of a hydroelectric power plant

KKTM 10

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

Fluid dynamics deals with the force needed to push a fluid inside a conduit or past a solid
surface. An example:

(a) Car manufacturers advertise how aerodynamically efficient their vehicles are.
Fluid mechanics principles are used to estimate the drag force on a car and to
suggest way to modify the car body shape.

(b) In the dam (Figure 1-6) used for hydroelectric power generation, a pipe (the
penstock) conveys the water from reservoir to water turbine, which extracts
energy from the flowing water. Fluid mechanics principles are used to calculate
the size of penstock, the water turbine, and the power that can be extracted
from the flowing water.

Example 1.8:
Question:
What is fluid mechanics?
Solution:
In general, fluid mechanic is associated with fluids at rest and addressing relative
motion between a fluid and a solid surface.

Example 1.9:
Question:
List of fluid mechanic types?
Solution:
a. Hydrostatics or Fluid Statics
b. Fluid Dynamics

EXERCISE 1.4

1. Explain the fluid dynamics used in airplane.
2. List of fluid statics used in vehicle.

KKTM 11

INTRODUCTION TO THERMAL AND FLUIDS ENGINEERING

SUMMARY

In countless engineering system, some aspect of thermodynamics, heat transfer, and fluid
mechanics is used. In this chapter we have studied that:

1. The principles and tools from all the three disciplines are required in the
development of solution to a design and/or analysis of a system.

2. Three steps are required to design any examples to model or investigate a system
performance; as follow:
a. The problem must be given thought, information organized and a solution
approach considered.
b. Fundamental concepts, equations, and definitions must be used.
c. The properties of the substances used in the problem must be evaluated.

REFERENCES

a. Kaminsky D. A, Jensen M. K., (2005), “Introduction to Thermal and Fluid
Engineering”, John Wiley & Sons, Inc.

b. Eastop, T.D, McConkey, A., (2004), 5th Edition, “Applied Thermodynamics for
Engineering Technologist”, Longman.

c. Yunus, A.C, Michael, A.B., (2002), 4th Edition, “Thermodynamics, an Engineering
Approach”, Mc Graw Hill, New York.

d. D.F. Young, B.R. Munson, T.H. Okiishi, (2004), “Fundamental of Fluid Mechanics”,
4th Edition, John Wiley & Sons, Inc.

KKTM 12

CHAPTER 2

THE FIRST LAW OF THERMODYNAMICS

THE FIRST LAW OF THERMODYNAMICS

CHAPTER 2: THE FIRST LAW OF THERMODYNAMICS

INTRODUCTION

Thermodynamics is a branch of physics that deals with the energy and work of a system.
Thermodynamics deals only with the large-scale response of a system, which we can
observe, and measure in experiments. Small-scale gas interactions are described by the
kinetic theory of gases.

There are three principal laws of thermodynamics, which are described on separate slides.
Each law leads to the definition of thermodynamic properties, which help us to understand
and predict the operation of a physical system.

We will present some simple examples of these laws and properties for a variety of physical
systems, although we are most interested in the thermodynamics of propulsion systems and
high speed flows. Fortunately, many of the classical examples of thermodynamics involve
gas dynamics.

In our observations of the work done on, or by a gas, we have found that the amount of
work depends not only on the initial and final states of the gas but also on the
process, or path which produces the final state.

Similarly the amount of heat transferred into, or from a gas also depends on the initial
and final states and the process, which produces the final state. Many observations of
real gases have shown that the difference of the heat flow into the gas and the work done by
the gas depends only on the initial and final states of the gas and does not depend on the
process or path that produces the final state.

This suggests the existence of an additional variable, called the internal energy of the gas,
which depends only on the state of the gas and not on any process. The internal energy is a
state variable, just like the temperature or the pressure.

The first law of thermodynamics defines the internal energy (E) as equal to the difference of
the heat transfer (Q) into a system and the work (W) done by the system.

E2 - E1 = Q - W

We have emphasized the words "into" and "by" in the definition. Heat removed from a
system would be assigned a negative sign in the equation. Similarly work done on the
system is assigned a negative sign.

KKTM 13

THE FIRST LAW OF THERMODYNAMICS

Figure 2.1 Thermodynamic system in equilibrium state

The internal energy is just a form of energy like the potential energy of an object at some
height above the earth, or the kinetic energy of an object in motion. In the same way that
potential energy can be converted to kinetic energy while conserving the total energy of the
system, the internal energy of a thermodynamic system can be converted to either kinetic or
potential energy.

Like potential energy, the internal energy can be stored in the system. Notice, however, that
heat and work cannot be stored or conserved independently since they depend on the
process. The first law of thermodynamics allows for many possible states of a system to
exist, but only certain states are found to exist in nature.

LEARNING OBJECTIVES

At the end of this chapter, you should be able to:

1. Describe the nature of internal energy.
2. Explain the first law of thermodynamics, energy balances, and mechanisms of energy

transfer to or from a system.
3. Describe the hypothetical substance “ideal gas” and the ideal-gas equation of state.

KKTM 14

THE FIRST LAW OF THERMODYNAMICS

2.1 THE FIRST LAW OF THERMODYNAMICS

The central organizing idea of thermodynamics is the principle of conservation of
energy. This one idea is vital to understanding an enormous range of processes. In
the absence of nuclear reactions, in which mass is converted to energy, total energy
is always conserved under all circumstances, regardless of the form of energy.

Conservation of energy is so important in thermodynamics that it is called the first
law of thermodynamics. In this chapter, the first law for a closed system will be
introduced. As defined earlier, a closed system consists of a fixed amount of mass.
No mass enters or leaves the system.

In a closed system, the first law may be expressed as

E  Q  W (2-1)

Where  E is the change in all forms of energy stored in the system, Q is the net
energy that is added to the system in the form of heat, and W is the net energy that
leaves the system in the form of work. Eq. 2-1 applies to a process that takes place
over a finite time interval. The quantity Q is the net heat that is added during this time
interval, and the quantity W is the net work done during the time interval; Q and W
could be positive or negative depending on the direction of the net energy flow of
each quantity.

The change in stored energy,  E, is the difference between the energy of the
system at the end of the process and the energy of the system at the start of the
process.

A simple schematic that illustrates the first law for a closed system is shown in Figure
2-2. The system is the mass contained within the dotted line. Heat and work are
forms of energy that cross the system boundary, while E is a form of energy that is
stored within the system boundary. The first law is a balance among these various
forms of energy.
It states that:

 change    energy    energy 
 in     
 energy   entering   leaving 

The first law of thermodynamics, also known as the conservation of energy principle,
provides a sound basis for studying the relationships among the various forms of
energy and energy interactions.

Based on experimental observations, the first law of thermodynamics states that
energy can be neither created nor destroyed; it can only change forms. Therefore,
every bit of energy should be accounted for during a process.

KKTM 15

THE FIRST LAW OF THERMODYNAMICS

Figure 2.2 The stored energy in this closed system changes from E1 to E2 as time
goes from t1 to t2 (ΔE = E2 – E1). Q is the net energy entering as heat
between t1 and t2, while W is the net energy leaving as work between t1
and t2.

The energy, E, stored in the system consists of three components: kinetic energy,

potential energy, and internal energy. Kinetic energy, KE, is due to the velocity of the

system and has a magnitude given by

KE  1 mV 2 (2-2)
2

where m is the total mass and V is the magnitude of the velocity of the system
relative to an inertial reference frame. In this text the magnitude of the velocity vector
will always be designated as V to distinguish it from volume, v.

Potential energy, PE, is due to the elevation of the system in a gravitational field and
is given by

PE = mgz (2-3)

Where g is the acceleration of gravity and z is the elevation above a reference plane.

Internal energy, U, is energy stored at a molecular or atomic level. There is no simple
expression for internal energy that applies to all cases. In single-phase materials
such as solids, liquids, or gases, the internal energy depends primarily on the
temperature. Internal energy is also stored in chemical bonds and in the attractive
forces between the molecules of solids and liquids.

If kinetic, potential, and internal energy are substituted into Eq. 2-1, the result is:

KE  PE  U  Q  W (2-4)

KKTM 16

THE FIRST LAW OF THERMODYNAMICS

where  KE is the change in kinetic energy,  PE is the change in potential energy,
and  U is the change in internal energy of the system. Much of the discussion in
this chapter and the next is devoted to explaining each of the five forms of energy in
Eq. 2-4 and showing how they interact in a wide variety of applications. This
approach develops an intuitive understanding of the first law and will be a useful
introduction to the study of thermal and fluid systems.

Example 2.1:
Question:
What is the first law of thermodynamics?
Solution:
The first law of thermodynamics is conservation of energy where provides a sound
basis for studying the relationships among the various forms of energy and energy
interactions.

Example 2.2:
Question:
List of three components energy stored in the system.
Solution:
1. Kinetic energy
2. Potential energy
3. Internal energy

KKTM 17

THE FIRST LAW OF THERMODYNAMICS

EXERCISE 2.1

1. A 2000-kg car accelerates from 20 to 60 km/h on an uphill road as shown in

Figure below. The car travels 120 m and the slope of the road from the horizontal
is 25o. Determine the work done by the engine.

2. A missile is launched vertically upward from the surface of the earth with an initial

velocity of 350 m/s. If the missile mass is 1200 kg, calculate the maximum height
the missile will attain. Assume no aerodynamic drag or other work during the flight
and no heat transfer.

KKTM 18

THE FIRST LAW OF THERMODYNAMICS

2.2 INTERNAL ENERGY

When energy is added to or removed from a system, changes in system properties
occur. For example, if energy (either heat or work) is added to a copper block, its
temperature will rise. On a microscopic level, the energy that flows into the block
causes more energetic vibrations of the copper molecules, and temperature depends
on these vibrations.

On the other hand, energy addition does not always result in a temperature increase.
If heat is transferred to a block of ice at 0oC, it melts into liquid water, but its
temperature does not change. In this case, the heat transfer to the ice breaks the-
bonds in the solid structure and causes the solid to liquid.

In order to understand changes such as these, the concept of internal energy was
invented. Internal energy is energy stored in the material. It can take many forms. In
a solid, energy is stored in the vibrations of the atoms about their equilibrium
positions.

When energy flows into a solid due to heat transfer, that energy is stored as internal
energy. The increased internal energy is manifested either in increased vibrations or
in a change of phase. If vibrations increase, temperature rises; if bonds are broken,
temperature remains constant.

In addition to these examples, there are many other forms of internal energy. The
chemical bonds between the atoms in a molecule contain internal energy. In a gas,
the translation of the molecules, the rotation of the molecules about their centre of
mass, and the internal vibrations of the molecules all contribute to the internal
energy. Internal energy is also stored in the nuclei of atoms.

Internal energy can be referred as the store of energy, which results from the random
motion of atoms and molecules of a body. At any particular state, the atoms and
molecules will have a particular overall degree of random motion and, in pure
substance; this degree of random motion will be the same each time the substance
returns to that state. The degree of random motion must therefore be a property.
Internal energy is a function of the degree of random motion, so it must be a
property.

Internal energy is defined as the energy associated with the random, disordered
motion of molecules. It is separated in scale from the macroscopic ordered energy
associated with moving objects; it refers to the invisible microscopic energy on the
atomic and molecular scale. For example, a room temperature glass of water sitting
on a table has no apparent energy, either potential or kinetic as shown in Figure 2-3.

KKTM 19

THE FIRST LAW OF THERMODYNAMICS
But on the microscopic scale it is a seething mass of high-speed molecules traveling
at hundreds of meters per second. If the water were tossed across the room, this
microscopic energy would not necessarily be changed when we superimpose an
ordered large-scale motion on the water as a whole.

U is the most common symbol used for internal energy.

Figure 2-3 Example of internal energy

Example 2.3:
Question:
Explain the internal enegy occurs in the system.
Solution:
When energy is added to or removed from a system, changes in system properties
occur. For example, if energy (either heat or work) is added to a copper block, its
temperature will rise.

KKTM 20

THE FIRST LAW OF THERMODYNAMICS

Example 2.4:
Question:
What is energy stored when energy flows into a solid due to heat transfer?
Solution:
When energy flows into a solid due to heat transfer, that energy is stored as internal
energy. The increased internal energy is manifested either in increased vibrations or
in a change of phase. If vibrations increase, temperature rises; if bonds are broken,
temperature remains constant.

EXERCISE 2.2

1. As shown in Figure below, when heat is added to the tank, and the temperature
raises 12oC. Explain:
a. The 1st law, if we add 5 J of heat to the liquid as shown in Figure (a)
b. The 1st law, if we add 5 J of shaft work as shown in Figure (b)

KKTM 21

THE FIRST LAW OF THERMODYNAMICS

2.3 SPECIFIC HEAT OF IDEAL LIQUIDS AND SOLIDS

The specific heat is defined, as the energy required raising the temperature of a unit
mass of a substance by one degree. In general, this energy will depend on how the
process is executed. In thermodynamics, we are interested in two kinds of specific
heats: specific heat at constant volume Cv and specific heat at constant pressure Cp.

A substance whose specific volume (or density) is constant is called an
incompressible substance. The specific volumes of solids and liquids essentially
remain constant during a process. Therefore, liquids and solids can be approximated
as incompressible substances without sacrificing much in accuracy. The constant-
volume assumption should be taken to imply that the energy associated with the
volume change is negligible compared with other forms of energy.

It can be mathematically shown that the constant-volume and constant-pressure
specific heats are identical for incompressible substances. Therefore, for solids and
liquids, the subscripts on Cp and Cv can be dropped, and both specific heats can be
represented by a single symbol C. That is,

Cp = Cv = C

This result could also be deduced from the physical definitions of constant-volume
and constant-pressure specific heats.

Figure 2-4 shows the heat is added to the tank and the temperature will rise. The
temperature will also rise if work is done on the liquid, even if there is no heat
transfer.

For the constant specific heat, the formula is:

U  mcT

Figure 2-4 In case (a), heat is added to a liquid in a tank. In case (b), shaft work is
done on a liquid in this insulated (adiabatic) tank. In this case, we also assume
insignificant heat transfer between the liquid and the paddlewheel blades.

KKTM 22

THE FIRST LAW OF THERMODYNAMICS

Example 2.5:
Question:
What is spesific heat?
Solution:
The specific heat is defined, as the energy required raising the temperature of a unit
mass of a substance by one degree. In general, this energy will depend on how the
process is executed.

Example 2.6:
Question:
List of two kinds of specific heat.
Solution:
1. Specific heat at constant volume Cv
2. Specific heat at constant pressure Cp.

EXERCISE 2.3

1. A 0.5 kg silver (c=0.235 kJ/kg.oC) ball is dropped from a height of 60 m. It
becomes embedded in the ground. Estimate the temperature rise of the ball just
after impact.

KKTM 23

THE FIRST LAW OF THERMODYNAMICS

2.4 FUNDAMENTAL PROPERTIES

Any characteristic of a system in equilibrium is called a property. The 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.

Some Extensive Properties:
a. Mass
b. Volume
c. Total energy
d. Mass dependent property

Intensive properties are those that are independent of size.

Some Intensive Properties:
a. Temperature
b. Pressure
c. Age
d. Color
e. Any mass independent property

Extensive properties per unit mass are intensive properties. For example, the
specific volume v, defined as

and density ρ, defined as

are both intensive properties.

KKTM 24

THE FIRST LAW OF THERMODYNAMICS

Example 2.7:
Question:
What is fundamental property.
Solution:
A fundamental property is any characteristic of a system in equilibrium.

Example 2.8:
Question:
List of extentive properties.
Solution:
Some Extensive Properties:

a. Mass
b. Volume
c. Total energy
d. Mass dependent property

EXERCISE 2.4

1. A gas is contained in a piston-cylinder assembly as shown in the figure below. A
compressed spring exerts a force of 60 N on the top of the piston. The mass of
the piston is 4 kg, and the surface area is 35 cm2. If atmospheric pressure is 95
kPa, what is the pressure of the gas in the cylinder?

KKTM 25

THE FIRST LAW OF THERMODYNAMICS

2.5 IDEAL GASES

An ideal gas is defined as one in which all collisions between atoms or molecules are
perfectly elastic and in which there are no intermolecular attractive forces. One can
visualize it, as collections of perfectly hard spheres, which collide but which
otherwise, do not interact with each other. In such a gas, all the internal energy is in
the form of kinetic energy and any change in internal energy is accompanied by a
change in temperature.
An ideal gas can be characterized by three state variables: absolute pressure (P),
volume (V), and absolute temperature (T).
Based on our experience in chemistry and physics we recall that the combination of
Boyle’s and Charles’ laws for gases at low pressure result in the equation of state for
the ideal gas as

where R is the constant of proportionality and is called the gas constant and takes
on a different value for each gas. If a gas obeys this relation, it is called an ideal gas.
We often write this equation as

The gas constant for ideal gases is related to the universal gas constant valid for all
substances through the molar mass (or molecular weight). Let Ru be the universal
gas constant. Then,

The mass, m, is related to the moles, N, of substance through the molecular weight
or molar mass, M, see Table A-1. The molar mass is the ratio of mass to moles and
has the same value regardless of the system of units.

Since 1 kmol = 1000 gmol or 1000 gram-mole and 1 kg = 1000 g, 1 kmol of air has a
mass of 8.97 kg or 28,970 grams.

The ideal gas equation of state may be written several ways.

KKTM 26

THE FIRST LAW OF THERMODYNAMICS

Here,

P = absolute pressure in MPa, or kPa
v = molar specific volume in m3/kmol
T = absolute temperature in K
Ru = 8.314 kJ/(kmolꞏK)

Some values of the Universal Gas Constant, Ru, are

8.314 kJ/(kmolꞏK)
8.314 kPaꞏm3/(kmolꞏK)
1.986 Btu/(lbmolꞏR)
1545 ftꞏlbf/(lbmolꞏR)
10.73 psiaꞏft3/(lbmolꞏR)

The ideal gas equation of state can be derived from basic principles if one assumes:
1. Intermolecular forces are small.
2. Volume occupied by the particles is small.

Example 2.9:

Question:

What is definiton of ideal gas.

Solution:

An ideal gas is defined as one in which all collisions between atoms or molecules are
perfectly elastic and in which there are no intermolecular attractive forces.

KKTM 27

THE FIRST LAW OF THERMODYNAMICS

Example 2.10:
Question:
List of three state variables of an ideal gas.
Solution:
An ideal gas can be characterized by three state variables:
1. Absolute pressure (P)
2. Volume (V)
3. Absolute temperature (T).

EXERCISE 2.5

1. Find the density of hydrogen at a pressure of 150 kPa and a temperature of 50oC.
2. A piston-cylinder assembly contains 0.49 g of air at a pressure of 150 kPa. The

initial volume is 425 cm3. The air is then compressed while 16.4 J of work are
done and 3.2 J of heat are transferred to the surroundings. Calculate the final air
temperature.

KKTM 28

THE FIRST LAW OF THERMODYNAMICS

2.6 WORK

The first law is relationships among work, heat, and changes in stored energy. There
are many different kinds of work, including shaft work, expansion work, and electrical
work. Work is energy expended by force acting through a distance.
Thermodynamic work is defined as energy in transition across the system boundary
and is done by a system if the sole effect external to the boundaries could have been
the raising of a weight.
Mathematically, the differential of work is expressed as

here Θ is the angle between the force vector and the displacement vector. As with
the heat transfer, the Greek symbol δ means that work is a path-dependent function
and has an inexact differential. If the angle between the force and the displacement
is zero, the work done between two states is

Work has the units of energy force times displacement or Newton times meter or
joule (we will use kilojoules). Work per unit mass of a system is measured in kJ/kg.

Figure 2-5 A body moving in the direction s.

Figure 2-5 shows the velocity vector and the force vector are both in the same
direction. The general case in which the velocity vector and the force vector are in
different directions is not usually important in thermal and fluids engineering and will
not be discussed. An example of practical situation in which the net force vector is in
the direction of motion is shown in Figure 2-6, where a crate is being lifted against
the force of gravity.

KKTM 29

THE FIRST LAW OF THERMODYNAMICS

Figure 2-6 Force and motion in the same direction.

Example 2.10:
Question:
What is definition of thermodynamic work?
Solution:
Thermodynamic work is defined as energy in transition across the system boundary
and is done by a system if the sole effect external to the boundaries could have been
the raising of a weight.

Example 2.11:
Question:
List kinds of work.
Solution:
1. Shaft work
2. Expansion work
3. Electrical work.

KKTM 30

THE FIRST LAW OF THERMODYNAMICS

EXERCISE 2.6

1. Air at 30oC is contained in a piston-cylinder assembly. The piston has a weight of
15 N and a cross-sectional area of 0.12 m2. The initial volume of air is 3.5 m3.
Heat is added until the volume of the air becomes 6.5 m3. Atmospheric pressure
is 100 kPa.
a. Find the final air temperature
b. Determine the work done by the air on both the piston and the atmosphere

KKTM 31

THE FIRST LAW OF THERMODYNAMICS

2.7 SPECIFIC HEAT OF IDEAL GASES

In the case of compressible substances, two different types of specific heat are used.
To illustrate these, consider the two cases shown in Figure 2-7. In case (a), heat is
added to ideal gas in a rigid tank. We define the gas as the system. During this
process, the volume of gas remains constant and no work is done; furthermore, the
kinetic energy and potential energy of the system remain unchanged. From the first
law,

U=Q-W

Since no work is done, the work is zero, and this becomes

U =Q

Figure 2-7 Addition of heat to an ideal gas (a) in a constant volume process
and (b) in a constant pressure process.

If the gas is an ideal gas, then it can be shown experimentally that the internal
energy is only a function of temperature. A specific heat can be defined for gases in
much the same way as the specific heat, c, was defined for solids and liquids. If the
gas specific heat is constant and the gas has mass, m, then the change in internal
energy can be related to temperature change by

U  mcV T Constant specific heat, ideal gas

where Cv is called the specific heat at constant volume. Its name arises from the fact
that it is the proportionality constant when heat is added at constant volume, as in
the case just described. However, Cv has much broader application than just to this
one restricted case. This equation applies to all processes of an ideal gas with
constant specific heat and is not restricted to constant volume processes.

KKTM 32

THE FIRST LAW OF THERMODYNAMICS

U  mcpT Constant specific heat, ideal gas

where Cp is called the specific heat at constant pressure. It is the proportionally
constant that determine how much the gas temperature rises when the gas is heated

at constant pressure. However, Cp is not limited in usefulness just to constant-
pressure process.

Relationship between Cp and Cv for ideal gases is given by the following equation;

Cp = Cv + R (kJ/kgꞏK)

This is an important relationship for ideal gases since it enables us to determine Cv
from a knowledge of Cp and the gas constant R.

When the specific heats are given on a molar basis, R in the above equation should
be replaced by the universal gas constant Ru.

C p  Cv  Ru (kJ/kmolꞏK)

At this point, another ideal-gas property is introduced called the specific heat ratio k,
defined as

k  Cp
Cv

The specific heat ratio also varies with temperature, but this variation is very mild.
For monatomic gases, its value is essentially constant at 1.667. Many diatomic
gases, including air, have a specific heat ratio of about 1.4 at room temperature.

KKTM 33

THE FIRST LAW OF THERMODYNAMICS

Example 2.12:
Question:
If the gas is an ideal gas, what is function of the internal energy?
Solution:
If the gas is an ideal gas, then it can be shown experimentally that the internal
energy is only a function of temperature.

EXERCISE 2.7

1. A rigid tank contains 0.05 kg of air at 800 K and 300 kPa. The tank is cooled while
6.35 kJ of heat are transferred. Find the final air temperature and pressure
assuming variable specific heat.

KKTM 34

THE FIRST LAW OF THERMODYNAMICS

SUMMARY

In the first law of thermodynamics, conservation of energy is so important in
thermodynamics that it is called the first law of thermodynamics. In this chapter, the first law
for a closed system is introduced.

1. There are three types of stored energy considered in first law of thermodynamics,
a. Internal Energy
b. Kinetic Energy
c. Potential Energy

2. In using the first law, the signs of the work and heat terms are important.
a. The sign convention for work
i. Work done by a system is positive
ii. Work done on a system is negative

b. The sign convention for heat
i. Heat transfer to a system is positive
ii. Heat transfer from a system is negative

REFERENCES

a. Kaminsky D. A, Jensen M. K., (2005), “Introduction to Thermal and Fluid
Engineering”, John Wiley & Sons, Inc.

b. Eastop, T.D, McConkey, A., (2004), 5th Edition, “Applied Thermodynamics for
Engineering Technologist”, Longman.

c. Yunus, A.C, Michael, A.B., (2002), 4th Edition, “Thermodynamics, an Engineering
Approach”, Mc Graw Hill, New York.

d. D.F. Young, B.R. Munson, T.H. Okiishi, (2004), “Fundamental of Fluid Mechanics”,
4th Edition, John Wiley & Sons, Inc.

KKTM 35

THE FIRST LAW OF THERMODYNAMICS

KKTM 36

CHAPTER 3

THERMODYNAMICS PROPERTIES

THERMODYNAMIC PROPERTIES

CHAPTER 3 THERMODYNAMIC PROPERTIES

INTRODUCTION

Problems in thermal-fluids engineering often involve properties such as temperature,
pressure, density, internal energy, and enthalpy. These properties have been used
extensively in prior chapters and will continue to be important in present and next
chapters. In this chapter, the limitations of the ideal gas model are discussed and
alternatives for real gas behaviour are presented.

In addition, for all processes discussed thus far, substances have remained in the same
phase such as solid, liquid, or gas. For example, while gas temperature may have
decreased in a problem, the gas remained a gas at the end of the process and did not
condense into a liquid state. However, the processes involving phase change are
described, and methods to evaluate the properties substances changing phase are
presented. Examples of first-law applications with boiling, condensation, sublimation,
freezing, and other phase-change processes are given.

LEARNING OUTCOMES

At the end of this topic, you should be able to:

1. Introduce the concept of a pure substance.
2. Discuss the physics of phase-change processes.
3. Demonstrate the procedures for determining thermodynamic properties of pure

substances from tables of property data.

3.1 PROPERTIES OF PURE SUBSTANCES

We now turn our attention to the concept of pure substances and the
presentation of their data.

3.1.1 SIMPLE SYSTEM

A simple system is one in which the effects of motion, viscosity, fluid
shear, capillarity, anisotropic stress, and external force fields are absent.

3.1.2 HOMOGENEOUS SUBSTANCE

A substance that has uniform thermodynamic properties throughout is
said to be homogeneous.

KKTM 3

THERMODYNAMIC PROPERTIES

3.1.3 PURE SUBSTANCE

A pure substance has a homogeneous and invariable chemical
composition and may exist in more than one phase.

Examples:
(a) Water (solid, liquid, and vapor phases)
(b) Mixture of liquid water and water vapor
(c) Carbon dioxide, CO2
(d) Nitrogen, N2
(e) Mixtures of gases, such as air, as long as there is no change of

phase.

3.1.4 STATE POSTULATE

Again, the state postulate for a simple, pure substance states that the
equilibrium state can be determined by specifying any two independent
intensive properties.

3.2 INTERNAL ENERGY AND ENTHALPY IN TWO-PHASE
SYSTEM

For an ideal gas, internal energy, u, and enthalpy, h, are only functions of
temperature. However, in general in the single-phase regions, u and h depend on
temperature and pressure, though the variation with pressure is often small. The
internal energy per unit mass is called the specific internal energy and specific
volume; v is the volume per unit mass. Similarly, h is the enthalpy per unit mass,
that is,

vV uU h H
mm m

where m is the total mass of the system.

In a two-phase region, specific volume results from the mass-weighted average
of the saturated liquid and saturated vapour specific volumes. In like manner, the
internal energy of a mixture is also a mass-weighted average. For example, in
the liquid-vapour two-phase region, the specific internal energy of the liquid
phase is denoted as uf, while the specific internal energy of the vapour phase is
ug. The specific internal energy of the mixture is

u = (1 – x)uf + xug
= uf + x(ug – uf)
= uf + xufg

Enthalpy in the two-phase region is given by a similar set of equations as
h = (1 – x)hf + xhg
= hf + x(hg – hf)
= hf + xhfg

KKTM 3

THERMODYNAMIC PROPERTIES

where hfg = hg – hf is called the enthalpy of vaporization or heat of vaporization.

Finally, the equation can be written as

x  mg  v  v f  u  u f  h  hf
m f  mg vg  v f ug  u f hg  hf

Example 3.1:

A vial of volume 280 cc contains a two-phase mixture of steam and water
at 30oC. The quality is 0.45. Find the mass in grams.

Solution:

v  v f  x(vg  v f )  0.001004  0.45(32.89  0.001004)

14.8 m3 / kg

mV  280 /1000000  1.89x105 kg
v 14.8

EXERCISE 3.1

1. A container of volume 0.047 m3 is filled with 6.7 kg of steam at 600°C. Calculate
the system pressure.

2. Determine the volume, in m3, of 0.23 kg of H O at a temperature of 150oC and
2
(a) a pressure of 0.2 MPa
(b) a quality of 0.6
(c) a pressure of 5 MPa

3.3 PROPERTIES OF REAL LIQUIDS AND SOLIDS

Ideal liquids and solids are, by definition, incompressible. Their densities are
constant under all conditions. Ordinarily this is very good assumption; however,
there are some important exceptions. The expansion of liquid mercury as a
function of temperature is the principle used in making thermometers. Bridges
are constructed with expansion joints to allow the roadway to increase in size
without buckling as temperature increases. The density of seawater is elevated
at great depths.

KKTM 3

THERMODYNAMIC PROPERTIES

As in ideal gases, the internal energy of ideal solids and liquids depends only on
temperature. In differential form

du  cv dT

If cv is not a function of temperature,

u  cv T

The enthalpy of an ideal gas depends only on temperature. By definition,
h = u + Pv

For a process that starts at state 1 and ends at state 2,

h1 = u1 + P1v1
h2 = u2 + P2v2

If we assume an ideal solid or liquid, the volume does not change and
v1 = v2 = v

The difference in enthalpy is then
h2 – h1 = u2 – u1 + v (P2 – P1)

The internal energy, u, is a function only of temperature for an ideal solid or
liquid; however, the enthalpy depends on pressure as well. For an isothermal
process, u1 = u2 and equation reduces to

h2 – h1 = v (P2 – P1)

Consider the common process in which a solid or liquid is heated at a constant
pressure. For example, if an empty frying pan is heated on a range top, heat is
added at constant pressure. In this case, the metal expands as it heats. The
atmosphere presses on the frying pan and keeps it at constant pressure. The
heat is added in a constant-pressure process of a closed system is

Q = H2 – H1

The most accurate way to find the enthalpy in this equation is to use

thermodynamic tables. However, it is often more convenient to use specific heat

data. By definition, the specific heat at constant pressure is

cp(T, P)  h p
T

When enthalpy is a function only of temperature, this may be written as

cp(T, P)  h
T

Separating variables and integrating from state 1 to state 2 gives

 2 2 c p (T , P)dT
1
dh 

1

If we assume that cp is not a function of temperature or pressure, then
h2 – h1 = cp(T2 – T1)

KKTM 3

THERMODYNAMIC PROPERTIES

Substituting h = H/m, this becomes
H2 – H1 = mcp(T2 – T1)

As mentioned above, for a constant-pressure heating process, Q = H2 – H1;
therefore,

Q = mcp(T2 – T1)

This equation applies as long as cp is not a function of temperature. It can also be
used as approximation when cp is a function of temperature. In that case, the
value of cp at the average temperature of the process is used.

3.4 USE OF TABLES TO EVALUATE PROPERTIES

3.4.1 PHASE CHANGE PROCESSES OF PURE SUBSTANCES

Compressed liquid (sub cooled liquid) meaning liquid that is not about to
vaporize.

Saturated liquid is liquid that is about to vaporize.

Saturated liquid-vapor mixture (saturated mixture) when the liquid and
vapor phases coexist in equilibrium.

P = 1 atm P = 1 atm P = 1 atm
T =20oC T =100oC T =100oC

Heat Heat Heat

Figure 3.1 Figure 3.2 Figure 3.3
At 1 atm and 20oC, At 1 atm and 100oC, As more heat is
water exists in liquid water exists as a liquid transferred, part of the
phase (compressed that is ready to vaporize saturated liquid
vaporizes (saturated
liquid) (saturated liquid) liquid-vapor mixture)

KKTM 4

THERMODYNAMIC PROPERTIES

P = 1 atm P = 1 atm
T =100oC T =100oC

Heat Heat

Figure 3.4 Figure 3.5
At 1 atm pressure, the As more heat is
temperature remains transferred, the
temperature of the vapor
constant at 100oCC
until the last drop of starts to rise
liquid is vaporized (superheated vapor)

(saturated vapor)

P P = 1 atm

Compresse 2 Saturated 5
d Liquid Mixture Superheated
Vapor
3 4

1

v

Figure 3.6 T-v diagram for the heating process of water at constant pressure

3.4.2 PROPERTY TABLES

In addition to the temperature, pressure, and volume data, Tables of
saturated steam-water (temperature and pressure tables), superheated
vapor, and compressed liquid water contain the data for the specific
internal energy u the specific enthalpy h and the specific entropy s. The
enthalpy is a convenient grouping of the internal energy, pressure, and
volume and is given by

H = U + PV

The enthalpy per unit mass is
h = u + Pv

The enthalpy is useful in the energy balance during a constant pressure
process for a substance contained in a closed piston-cylinder device. The
enthalpy has units of energy per unit mass, kJ/kg. The entropy s is a
property defined by the second law of thermodynamics and is related to

KKTM 4

THERMODYNAMIC PROPERTIES

the heat transfer to a system divided by the system temperature; thus, the
entropy has units of energy divided by temperature.

3.4.3 SATURATED WATER TABLES

Since temperature and pressure are dependent properties using the
phase change, two tables are given for the saturation region. Table of
saturated steam-water (temperature table) has temperature as the
independent property; table of saturated steam-water (pressure table) has
pressure as the independent property. These two tables contain the same
information and often only one table is given.

KKTM 4

THERMODYNAMIC PROPERTIES

For the complete Property Table, the last entry is the critical point at
22.09 MPa.

Saturation pressure is the pressure at which the liquid and vapor
phases are in equilibrium at a given temperature.

Saturation temperature is the temperature at which the liquid and vapor
phases are in equilibrium at a given pressure.

The subscript fg used in Tables of saturated steam-water refers to the
difference between the saturated vapor value and the saturated liquid
value region.

That is,
ufg = ug - uf
hfg = hg - hf
sfg = sg - sf

The quantity hfg is called the enthalpy of vaporization (or latent heat of
vaporization). It represents the amount of energy needed to vaporize a
unit of mass of saturated liquid at a given temperature or pressure. It
decreases as the temperature or pressure increases, and becomes zero
at the critical point.

Example 3.2:

A rigid can contains 0.90 g of saturated water vapor at 450 kPa. Calculate
the volume of the can in cubic centimeters.

Solution:

P  0.45 MPa vg  0.414 m3 / kg

V  m.vg  (0.9 /1000).0.414  0.0003726 m3

KKTM 4

THERMODYNAMIC PROPERTIES

EXERCISE 3.2

1. A piston-cylinder assembly contains 0.15 kg of saturated steam at 130°C. The
piston is held in place by a weight. To reach the final state, 8300 J of heat is
added. Find the final temperature.

3.4.4 QUALITY AND SATURATED LIQUID-VAPOR MIXTURE

Now, let’s review the constant pressure heat addition process for water
shown in Figure 3.6. Since state 3 is a mixture of saturated liquid and
saturated vapor, how do we locate it on the T-v diagram? To establish the
location of state 3 a new parameter called the quality x is defined as

The quality is zero for the saturated liquid and one for the saturated vapor
(0 ≤ x ≤ 1). The average specific volume at any state 3 is given in terms of
the quality as follows. Consider a mixture of saturated liquid and
saturated vapor. The liquid has a mass mf and occupies a volume Vf. The
vapor has a mass mg and occupies a volume Vg.

Example 3.3:
A rigid tank contains 10 kg of water at 90oC. If 8 kg of the water is in the
liquid form and the rest is in the vapour form, determine:
(a) the pressure in the tank
(b) the volume of the tank

Solution:
(a) P  Psat @T 900 C  70.183 kPa

KKTM 4

THERMODYNAMIC PROPERTIES

x mg  (10  8)  0.2
mf  mg 10

v  v f  x(vg  v f )  0.001036  0.2(2.3593  0.001036)

(b)  0.473m3 / kg

V  mv  10.0.473  4.73m3

EXERCISE 3.3

1. A mixture of steam and water is contained in a rigid tank of volume 3050 cm3. The
mixture has a quality of 0.55 and a temperature of 120°C. Heat is added until the
temperature is 140°C. Find
(a) the final quality
(b) the amount of heat added

3.4.5 SUPERHEATED WATER TABLE

A substance is said to be superheated if the given temperature is greater
than the saturation temperature for the given pressure.

State 5 in Figure 3.6 is a superheated state.

In the superheated water table, T and P are the independent properties.
The value of temperature to the right of the pressure is the saturation
temperature for the pressure. The first entry in the table is the saturated
vapor state at the pressure.

KKTM 4

THERMODYNAMIC PROPERTIES

Superheated Vapor can be characterized by:
(a) Lower Pressures (P<Psat at a given T)
(b) Higher Temperatures (T>Tsat at a given P)
(c) Higher specific volume (v<vg at a given P or T)
(d) Higher internal energy (u<ug at a given P or T)
(e) Higher enthalpies (h<hg at a given P or T)

Example 3.4:

Superheated vapor at 1.4 Mpa and 250oC is allowed to cool at constant
volume until the temperature drops to 120oC. Determine:
(a) the initial specific volume
(b) the quality at the final state

Solution:

P1  1.4 MPa
(a) T1  250o C

v1  0.163 m3 / kg

v2  v1  0.163m3 / kg

T2  120o C
(b) v2  v f  x(vg  v f )

x  v2  v f  0.163  0.001060  0.182
vg  vf 0.8919  0.001060

KKTM 4