Mechanical Engineering

1. MechanicalEngineering Dr. Galal Mostafa Eng. Shenouda Tawfiek Department of Mechanical Power Engineering Faculty of Engineering, Cairo University 24 / 02 / 2010

2. Mechanical Engineering Lectures 2-3 Introductions Concepts, Definitions and First Law 24 / 02 / 2010

3. Mechanical Engineering Teaching Staff • Dr. Galal Mostafa • Mechanical Power Engineering Department • Office: Build # 11, 2nd floor, Mechanical Lab. Building • Tel: 018-690 42 44 • Email: air.comp.1@hotmail.com • Eng. Shenouda Tawfiek • Office: Build # 17, 3rd floor • Tel: 0103506329 • Email: eng_shenoda1@yahoo.com 24 / 02 / 2010

4. Mechanical Engineering Course load : First Part 50 Marks • Lecture/Section : 5 Marks • Reports/Assignment : 5 Marks • Mid-Term : 10 Marks • Final examination : 30 Marks Course load: Second Part 50 Marks 24 / 02 / 2010

5. Mechanical Engineering 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. 24 / 02 / 2010

6. Mechanical Engineering Definitions 24 / 02 / 2010

7. 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. 24 / 02 / 2010

8. 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.

9. 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. 24 / 02 / 2010

10. Mechanical Engineering 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) 24 / 02 / 2010

11. 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. 24 / 02 / 2010

12. Types of systems 24 / 02 / 2010

13. Mechanical Engineering 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. 24 / 02 / 2010

14. 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 24 / 02 / 2010

15. Mechanical Engineering • 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.

16. Mechanical Engineering 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

17. 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) 24 / 02 / 2010

18. 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 changetemperature. 24 / 02 / 2010

19. Vapour chart T : temperature v : specific volume p : pressure x : dryness fraction Critical point Ideal gas Compressed liquid Superheated vapour Saturated liquid Saturated vapour Wet vapour region 03 / 03 / 2010

20. Mechanical Engineering 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 )

21. 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 ifdone 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 .  03 / 03 / 2010

22. Mechanical engineering 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.

23. Mechanical engineering Absolute Pressure Pressure above atmosphere Pressure below atmosphere

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25. Mechanical engineering 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.

26. 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 ) + PBπ RB2 2 *10 5 * π (0.05)2 + 9*9.806 = 1*10 5 * π [ ( 0.05)2 – (0.0125)2 ] + PBπ (0.0125)2 PB = 18.8 bar

27. Mechanical engineering IDEAL GAS

28. Mechanical engineering 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 : P v = R T The ideal gas equation of state, for the total gas mass becomes : m P v = m R T P V = n M R T P V = n R T

29. Mechanical engineering 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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31. 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 [ ∆U ]12 = U2 - U1 H = U + P V 03 / 03 / 2010

32. Mechanical engineering Thermodynamic processes

33. Mechanical engineering 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 = 03 / 03 / 2010

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37. Mechanical engineering First low of thermodynamic Energy equation Conservation of Energy 03 / 03 / 2010

38. 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”

39. 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

40. 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. 03 / 03 / 2010

41. 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. 03 / 03 / 2010

42. 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. 03 / 03 / 2010

43. 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

44. 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

45. 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.

46. 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

47. 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

48. 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 dE = dU + dK.E + dP.E = dQ - dW

49. Mechanical engineering • The integrated form of the first law equation is : where :

50. 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.