Download Mechanical Engineering

Dr. Galal Mostafa
Eng. Shenouda Tawfiek
Department of Mechanical Power Engineering
Faculty of Engineering, Cairo University
24 / 02 / 2010
Lectures 2-3
Introductions
Concepts, Definitions and First Law
24 / 02 / 2010
Teaching Staff
 Dr.
Galal Mostafa
 Mechanical Power Engineering Department
 Office: Build # 11, 2nd floor, Mechanical Lab. Building
 Tel: 018-690 42 44
 Email: [email protected]
 Eng.
Shenouda Tawfiek
 Office: Build # 17, 3rd floor
 Tel: 0103506329
 Email: [email protected]
24 / 02 / 2010
Course load
:
 Lecture/Section
:
 Reports/Assignment :
 Mid-Term
:
 Final examination
:
First Part 50 Marks
5 Marks
5 Marks
10 Marks
30 Marks
Course load: Second Part 50 Marks
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Examples:
1. Engines : convert heat from combustion to
shaft rotation (mechanical work).
2. Refrigerators : convert compressor work to
absorb heat from food.
3. Jet Engines : to produce thrust (aircraft).
4. Steam Power Plant : to produce electricity.
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Definitions
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Properties of Pure Substances
Such as mass, temperature, volume, and pressure
Pure substance : are those materials which are chemically fixed and
homogeneous throughout.
Properties : are used to define the current state of a substance. Several
and more properties exist to describe substances in thermodynamics.
Properties may be intensive, if they are point properties (properties that
related to the material) or extensive, if they depend on the amount of
matter in the system.
Examples of extensive properties of systems are mass of system, number
of moles of a substance in a system, and overall or total volume of a
system. These properties depend on how much matter of the system you
measure.
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Properties of Pure Substances
Such as mass, temperature, volume, and pressure


Examples of intensive properties are pressure, temperature,
density, volume per mass, molar volume (which is volume per
mole), and average molecular weight (or molecular mass).
These properties are the same regardless of how you vary the
amount of mass of the substance.
Properties are like the variables for substances in that their
values are all related by an equation. The relationship
between properties is expressed in the form of an equation
which is called an equation of state. Perhaps the most
famous state equation is the Ideal Gas Law.
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Volume
The “SI” unit for volume is m3. Volume is an extensive property, but both specific
volume ( volume per mass ) and molar volume are intensive properties since they
do not depend on the measured mass of the system. A process during which the
specific volume of the system remains constant is called an isochoric process.
Pressure
The “SI” unit for pressure is Pa (Pascal), which is equivalent to a N / (m2).
Pressure is an intensive property. A process in which pressure remains constant
is called isobaric process.
Temperature
The concept of temperature is fundamental and significant to thermodynamics. We
know that a body at high temperature will transfer energy to one at lower
temperature. Consider two bodies with different temperatures in contact with each
other. Net energy transfer will be from the hotter body to the colder body. At some
point, the net energy transfer will be zero, and the bodies are said to be in thermal
equilibrium. Bodies in thermal equilibrium are defined to have the same
temperature. A process during which temperature remains constant is called
isothermal process.
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Phase
Is defined as a quantity of matter that is
homogenous throughout. When more than
one phase is present, the phases are
separated from each other by the phase
boundaries.
Example: Ice and water are 2 phases (i.e. same
material but different structure)
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Mechanical Engineering
System
System, in thermodynamics, is a
volume of matter surrounded by a
boundary. System may be closed
or open, relative to mass crossing
its boundary or not.
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Types of systems
Open Systems Closed Systems Isolated Systems
Exchange of
contents with
surroundings
Yes
No
No
Exchange of
heat with
surroundings
Yes
Yes
No
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Processes
A change in the system state is called a process. When
the initial and final states of a process are the same,
the process is called a cycle. If a process can be run
in reverse with no change in the system as well as
surroundings, then the process is called a reversible
process. If a process is not reversible it is called an
irreversible process.
Several processes are described by the fact that one
property remains constant.
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Mechanical Engineering
Isothermal Process
An isothermal process is one in which the
temperature remains constant. Please note
that a process being isothermal does not imply
anything about the heat transferred or work
done, i.e. heat transfer may take place during
an isothermal process. An isothermal process
implies that the product of the volume and the
pressure is constant for an ideal gas. i.e. :
PV = Constant
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 Isobaric
process
 Isochoric
process
process is a constant-pressure
process is a constant-volume
 Cycle
When a system in a given initial
state goes through a number of different
changes of state or processes and finally
returns to its initial state, the system has
undergone a cycle.
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Heat



Heat is defined as the form of energy that is
transferred across the boundary of a system at a
given temperature to another system (or the
surroundings) at a lower temperature by virtue of the
temperature difference between the two systems.
Heat is the energy exchanged due to a temperature
difference. As with work, heat is defined at the
boundary of a system. Heat rejected by the system is
negative, while the heat absorbed by the system is
positive.
Units of heat (energy): Joule
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Heat, Q
• A form of energy that can be transferred as a result of a temperature difference
• Should be considered as a DISORDERED form of energy
• Can be measured in terms of the heat capacity. For example :
where cs is the specific heat capacity (i.e. the heat capacity per unit mass)
and cM is the molar heat capacity (i.e. the heat capacity per mole)
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Specific Heat
The specific heat of a substance is the amount of heat required to
rise a unit mass of the substance a unit temperature. In general, we
can only talk about the average specific heat, c = Q/mΔT. Since it
was customary to give the specific heat as a property in describing a
material, methods of analysis came to rely on it for routine
calculations. However, since it is only constant for some materials,
older calculations became very convoluted for newer materials.
Latent Heat
It can be seen that the specific heat as defined above will be
infinitely large for a phase change, where heat is transferred without
any change in temperature. Thus, it is much more useful to define a
quantity called latent heat, which is the amount of energy required to
change the phase of a unit mass of a substance at the phase change
temperature.
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Vapour chart
Critical
point
T : temperature
v : specific volume
p : pressure
x : dryness fraction
Ideal gas
Wet
vapour
region
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Work

Work is usually defined as a force “F” , in N, acting
through a displacement “x” , in m, where the
displacement is in the direction of the force. In
infinitesimal form :
dW = F dx
 The
unit for work is Joule (J). ( J = 1 N m )
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Work, w
• Work is done as a result of motion or mechanical change, i.e. a direct result
of the action of a force.
• Should be considered as an ORDERED form of energy.
• Mathematically given by : w = force x distance moved
• Note: work is designated NEGATIVE if done on the system
POSITIVE if done by the system
Since : Pext = Force / cross-sectional area
The Negative sign is due to the fact that dx is in the opposite direction of Pext
.
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Pressure
is usually defined as a force F acting
on unit area, F/A, N/m2
Pressure
In thermodynamics, we are concerned with
absolute pressure. Most pressures were
indicated by gauges or vacuum.
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Absolute Pressure
Pressure above atmosphere
Pressure below atmosphere
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Example 1:
The following figure shows a gas contained in two cylinders A
and B, connected by a piston of two different diameters. The
mass of the piston is 9 kg and the gas inside cylinder A is at
2 bar abs. Calculate the pressure inside cylinder B.
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Mechanical engineering
Solution
Since the piston is totally balanced, then :
∑F = 0
FA + Mp g = Fat + FB
PA AA + Mp g = Pat ( AA - AB ) + PB AB
2 *10 5 * π RA2 + Mp g = 1 *10 5 * π ( RA2 - RB2 ) + PB π RB2
2 *10 5 * π (0.05)2 + 9*9.806 = 1*10 5 * π [ ( 0.05)2 – (0.0125)2 ] + PB π
(0.0125)2
PB =
18.8 bar
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IDEAL GAS
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Ideal Gases behavior
From experimental observation it has been found that the p-v-T
behavior of gases at low density is closely given by the
following equation of state :
Pv= RT
The ideal gas equation of state, for the total gas mass becomes :
mPv = mRT
PV = nMRT
PV = nRT
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In which n is the number of kmol of gas, or :
: is the universal gas constant (proportionality
constant ), the value of which is constant for any
gas:
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Symbol
Meaning
Units
P
System Gas Pressure
N/m2
V
System Gas volume
M3
T
System Gas Temperature
K
R
Gas constant
J/Kg.K
Universal Gas constant = 8314
J/Kmol.K
m
Mass of gas in the system
kg
M
Molecular weight
kg/kmol
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State Functions:
A state function refers to a property whose 'value' depends solely on the
state of the system, and independent on the way by which this state is
achieved. In particular, the work done, w, and heat energy transferred, q,
are not state functions, whilst the internal energy U is. The most
commonly used feature of a state function, (U, for example), is that :
[ ∆U ]12 = U2 - U1
U
=
Cv
T
that is the change in ‘U ’ from state 1 to state 2 is the difference between
its values at state 2 (=U2) and at state '1' (=U1).
Another important property is that, any function which is solely composed
from other state functions or properties is also a state function. For
example, since U, P and V are state functions, the enthalpy ‘H ‘ defined
as below is also a state function.
H = Cp T
H = U + PV
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Thermodynamic processes
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1- Polytropic process
A polytropic process takes place, when the system undergoes a
change from a state to anther and the following relation is
valid :
The work done during this process can be calculated as follows :
W1-2 =
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First low of thermodynamic
Energy equation
Conservation of Energy
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Mechanical engineering

The first low of thermodynamics states that :
“Energy can neither be created or destroyed, it
can only be transformed from one form to
another”
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Mechanical engineering
The first low of thermodynamics, for the shown system undergoing a
certain process, states that :
Ein - Eout = ∆ Estored
System
Energy in
Energy out
Energy stored
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Mechanical engineering
The first law also states that, when heat and
work interactions take place between a closed
system and the environment ( surroundings ),
the algebraic sum of the heat and work
interactions for a cycle is zero.
This is
equivalent, for any closed cycle, to :
dQ + dW = 0
‘Q’ is the heat transferred, and ‘W’ is the work
done on or by the system. Since these are the
only ways energy can be transferred for the
shown closed system, this implies that the total
energy of the system in the cycle is constant.
One consequence of the statement is that the total
energy of the system is a property of the system.
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Mechanical engineering

When a car engine has transferred some
work to the car, the car’s speed is
increased, so we can relate the kinetic
energy increase to the work.

If a heater provides a certain amount of
heat transfer to a pot with water we can
relate the water temperature increase to
heat transfer.
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Mechanical engineering

In other applications, we can also see a
change in the state without any work or
heat transfer, such as a falling object that
changes KE at the same time it is changing
elevation.
The energy equation then relates the two forms of energy of
the object.
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Mechanical engineering
 We
therefore conclude that, this is a state function,
and hence it is a property of the system mass. This
property is the stored energy of the mass. Thus we
can write dE = Q – W which when integrated from
an initial state 1 to a final state 2, we have :
E2 - E1 = Q1-2 - W1-2
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Mechanical engineering

Note that a control mass may be made up of several different
subsystems, as shown. In this case, each part must be
analyzed and included separately in applying the first law,
where :
Ein - Eout = ∆ Estored
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Mechanical engineering


The physical significance of the property E is that
it represents all the energy of the system at the
given state.
This energy might be present in a variety of forms.
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Mechanical engineering

It is convenient to consider the bulk kinetic and
potential energies separately and then to consider
all the other energies of the control mass in a
single property that we call the “internal energy”
and to which we give the symbol U. Thus, in this
case, we have :
E = U + P.E + K.E
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Mechanical engineering

The kinetic and potential energy of the control
mass are associated with the coordinate frame that
we select and can be specified by the macroscopic
parameters of mass, velocity and elevation. The
internal energy U includes all other forms of energy
of the control mass and is associated with the
thermodynamic state of the system. The sum of all
the microscopic forms of energy is called internal
energy
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Mechanical engineering

The first law of thermodynamics for a change of state
may therefore be written as :
dE = dU + dK.E + dP.E = dQ - dW


This equation states that: as the control mass (system)
undergoes a change of state, energy may cross the
boundary as either heat or work, and each may be
positive or negative.
The net change in the total energy of the system will
be exactly equal to the net change in the energy that
crosses the boundary of the system
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Mechanical engineering

The integrated form of the first law equation is :
where :
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Mechanical engineering
Concluded remarks



The property E, the energy of the control mass, was specified.
Conservation of energy : the net change of the energy of the
control mass (system) is always equal to the net transfer of
energy crossing the boundary as heat and work.
This equation can give only changes in internal, kinetic
energy, and potential energy, by knowing the initial and final
states.
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Mechanical engineering
Example 2:
A tank containing a fluid is stirred by a
paddle wheel. The work input to the paddle
wheel is 5090 kJ. The heat transfer from the
tank to the environment is 1500 kJ.
Consider the tank and the fluid inside a
control surface and determine the change
in internal energy of this control mass.
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Mechanical engineering
Solution
Since there is no change in KE and PE:
U2 - U1 = Q1-2
- W1-2
U2 - U1 = -1500 - (-5090 )
= 3590 kJ
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