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Dr. Galal MostafaEng. Shenouda Tawfiek
Department of Mechanical Power EngineeringFaculty of Engineering, Cairo University
24 / 02 / 2010
Lectures 2-3
IntroductionsConcepts, Definitions and First Law
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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]
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Course load : First Part 50 Marks
Lecture/Section : 5 MarksReports/Assignment : 5 MarksMid-Term : 10 MarksFinal examination : 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 SubstancesSuch 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 SubstancesSuch 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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VolumeThe “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.
PressureThe “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.
TemperatureThe 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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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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Mechanical Engineering
System
Open Systems Closed Systems Isolated Systems
Exchange of contents with surroundings
Yes No No
Exchange of heat with
surroundingsYes Yes No
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Types of systems
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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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
Mechanical Engineering
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Isobaric process is a constant-pressure process
Isochoric process is a constant-volume process
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 HeatThe 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 HeatIt 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 changetemperature.
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Vapour chartC
ompr
esse
d liq
uid
Saturated vapour
Sat
ura
ted
liq
uid
Wet vapour region
Critical point
Ideal gas
Superheated vapour
T : temperaturev : specific volumep : pressurex : dryness fraction
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
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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• Note: work is designated NEGATIVE if done on the system POSITIVE if done by the system
Pressure
Pressure is usually defined as a force F acting on unit area, F/A, N/m2
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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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 ( RA
2 - RB2 ) + PB π RB
2
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
Mechanical engineering
IDEAL GAS
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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 :
P v = R T
The ideal gas equation of state, for the total gas mass becomes :
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Ideal Gases behavior
m P v = m R T
P V = n M R T
P V = n R T
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
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 = 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
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[ ∆U ]12 = U2 - U1
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 :
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First low of thermodynamicEnergy 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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The first low of thermodynamics, for the shown system undergoing a certain process, states that :
Mechanical engineering
Ein - Eout = ∆ Estored
System
Energy in Energy out
Energy stored
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.
Mechanical engineering
The energy equation then relates the two forms of energy of the object.
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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 :
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Mechanical engineering
E2 - E1 = Q1-2 - W1-2
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 :
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Ein - Eout = ∆ Estored
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 :
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E = U + P.E + K.E
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 :
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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dE = dU + dK.E + dP.E = Q - W
Mechanical engineering
The integrated form of the first law equation is :
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where :
Mechanical engineering
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
Concluded remarks
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
Mechanical engineering
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