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Thermodynamic notes 2

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  • 1. FIRST LAW OF THERMODYNAMICS<br />The first law of thermodynamics, an expression of the principle of conservation of energy, states that energy can be transformed (changed from one form to another), but cannot be created or destroyed. <br />Limitations of First law of thermodyanamics<br />First law states that energy only transforms from one form to another and energy balance is maintained. The law, however, fails to state the conditions under which energy conversions are possible. The law presumes that any change of a thermodynamic state can take place in either direction. However, this is not true; particularly in the inter-conversion of heat and work. Processes proceed spontaneously in certain directions but not in the opposite directions in real life, even though the reversal of processes does not violate the first law. <br />Example: 1. The temperature of liquid contained in a vessel rises when it is stirred by a stirrer. However, the paddle work cannot be restored on cooling the liquid to its original state. <br />2. Electric current flowing through a resistor produces heat. Electric current once dissipated as heat cannot be converted back to electricity.<br />The examples cited above indicates that:<br />
    • First law fixes the exchange rate between heat and work, and places no restrictions on the direction of change.
    • 2. Processes proceed spontaneously in certain directions, but reverse is not automatically attainable in real life even though the reversal of the process does not violate the first law.
    • 3. First law provides a necessary but not sufficient condition for a process to occur.
    • 4. There does exists some directional law which would tell whether a particular process occurs or not. This answer is provided by the second law of thermodynamics.
    First law for a closed system under going a cycle or <br />Joules experiment or <br />Verification of first law of thermodynamics or <br />Experiment to determine Joules equivalent (or mechanical equivalent of heat)<br />Consider a closed system which consists of a mass of water contained in an adiabatic vessel having a thermometer and stirrer, as shown in Figure 1.<br />Figure 1. Joules Experiment<br />Let the amount of work W1-2 be done upon the system by the stirrer through the pulley. The system was initially at temperature T1, the same as that of atmosphere, and after work transfer let the temperature rise to T2. The pressure is always 1atm. The process 1-2 undergone by the system is shown in Figure 2 in generalized thermodynamic coordinates X,Y (for example temperature, etc.). Let the insulation be now removed. The system and the surroundings interact by heat transfer till the system returns to the original temperature T1, attaining the condition of thermal equilibrium with the atmosphere. The amount of heat transferQ2-1 from the system during this process, 2-1, is shown in Figure 2, can be estimated. <br /> <br />Figure 2: Cycle completed by a system with two energy interactions: Adiabatic work transfer W1-2 followed by Heat Transfer Q2-1<br />The system thus executes a cycle, which consists of a definite amount of work input W1-2 to the system followed by the transfer of an amount of heat Q2-1 from the system. It has been found that this W1-2 is always proportional to the heat Q2-1, and the constant of proportionality is called the Joule’s equivalent or the mechanical equivalent of heat. In this example , there is only one heat and one work transfer. If the cycle involves many more heat and work quantities, the same result can be observed. Expressed algebraically,<br />Wcycle=J Qcycle<br />Where J is the Joule’s equivalent or the mechanical equivalent of heat. This can also be expressed in the form,<br />dW=JdQ<br />Where the symbol denotes the cyclic integral for the closed path. This is the first law of thermodynamics. <br />The constant of proportionality, J, is found to be unity (Nm/J).<br />Calorific theory of heat<br />Prior to J.P.Joule, heat was considered to be an invisible fluid flowing from a body of high calorie to a body of lower calorie and this was known as the caloric theory of heat. It was Joule who during the period 1840-1849 performed experiments and established that heat is a form of energy and laid the foundation for the first law of thermodynamics.<br />First law for a closed system undergoing a change of state or mathematical equation for first law of thermodynamics<br />Go, thru section 4.2, page 71 of “Engineering Thermodynamics”, fourth Edition, by P. K. Nag.<br />Energy- A property of the System<br />Consider a system which changes its state from state 1 to state 2 by following the path B (as shown in figure). So the system undergoes a cycle. Let ∆E be the change in energy of system, W be the work transfer by the system and Q be the heat transfer. Writing the First law of thermodynamics for Path A.<br />Energy as property of a System<br />QA = ∆ EA + WA <br />or, ∆ EA = QA –WA ......(1)<br />and for Path B<br />QB = ∆ EB + WB <br />or, ∆ EB = QB –WB ........(2)<br />The processes A and B together constitute a cycle, for which<br />( ∑ W )cycle = ( ∑ Q )cycle .......(3)<br />or WA + WB = QA + QB ....... (4)<br />or QA - WA = WB - QB ....... (5)<br />Substituting Eqs (1) and (2) in Eq(5).<br /> ∆ EA = -∆ EB .......(6)<br />Similarly, had the system returned from state 2 to state 1 by following the path C instead of path B,<br />∆ EA = -∆ EC ........(7)<br />From Eqs (6) and (7)<br />∆ EB = ∆ EA<br />Therefore, it is seen that the change in energy between two states of a system is the same, whatever path the system may follow in undergoing that change of state. If some arbitrary value of energy is assigned to state 2, the value of energy at state 1 is fixed independent of the path the system follows. Therefore, energy has a definite value for every state of the system. Hence, it is a point function and property of the system. Energy is an extensive property. Also dE=0, since for a cycle, property of a system is zero.<br />DIFFERENT FORMS OF ENERGY STORED<br />Energy is the capacity to do work. In thermodynamics, energy can be stored in two forms:<br />
    • Energy in transit:- Work and heat interactions are the forms of energy in transit, observed at the boundaries of a system. They are not properties of a system. They are path functions, their magnitudes depend upon the path the system follows during a change of state.
    • 5. Energy in storage:- Energy in storage is internal energy, is a point or state function and hence a property of a system.
    The symbol E refers to the total energy stored in a system. Basically there are two modes in which energy may be stored in a sytem:<br />
    • Macroscopic energy mode : The macroscopic energy mode includes the macroscopic kinetic energy and potential energy of a system.
    • 6. Macroscopic kinetic energy: Consider a fluid element of mass m having the mass velocity V (as shown in figure). The macroscopic kinetic energy EK of the fluid element by virtue of its motion is given by
    • 7. EK=mV22
    • 8. Macroscopic potential energy: If the elevation of the fluid element from an arbitrary datum is z, then the macroscopic potential energy EP by virtue of its position is given by
    • 9. EP=mgz
    • 10. where g is acceleration due to gravity.
    • 11. Microscopic energy mode : It refers to the energy stored in the molecular and atomic structure of the system, which is called the molecular internal energy or internal energy, it is denoted by U.
    • 12. Matter is composed of molecules. Molecules are in random thermal motion (for a gas) with some average velocity, v, constantly colliding with each other and the walls (as shown in figure). Due to collision, the molecules may be subjected to rotation as well as vibration. They can have translation kinetic energy, rotational kinetic energy, vibrational energy, electronic energy, chemical energy and nuclear energy. If ε represents the energy of one molecule, then
    • 13. ε=εtran+εrot+εvib+εchem+εelect+εnuclear
    • 14. If N is the total number of molecules in the system, then the total internal energy is given by
    • 15. U=Nε
    • 16. In an ideal gas there are no intermediate forces of attraction and repulsion, and the internal energy depends only on temperature. Thus,
    • 17. U=f(T)
    • 18. for an ideal gas.
    • 19. Other forms of energy which can be possessed by a system are magnetic energy, electrical energy and surface tension energy. In the absence of these forms, the total energy E of a system is given by
    • 20. E= Emacro+Emicro=EK+EP+U
    • 21. In the absence of motion and gravity; EK = 0, EP = 0
    • 22. ->E=U
    • 23. From the first law of thermodynamics,
    • 24. Q=∆E+W ......(1)
    • 25. Where Q is heat transfer,
    • 26. W = work transfer
    • 27. Since E=U
    • 28. The first law of thermodynamics reduces to
    • 29. Q=∆U+W .....(2)
    • 30. U is an extensive property of the system and specific internal u (=U/m) is intensive.
    • 31. Equation (1) and (2) in differential form can be written as
    • 32. dQ=dE+dW ......(3)
    • 33. dQ=dU+dW ......(4)
    • 34. where dW=dWpdV + dWshaft + dWelectrical +...................
    • 35. considering the different forms of work transfer which may be present. When only pdV work is present, the equations (3) and (4) becomes
    • 36. dQ=dE+pdV ......(5)
    • 37. dQ=dU+pdV ......(6)
    • 38. On integrating
    • 39. Q=∆E+pdV ......(7)
    • 40. Q=∆U+pdV ......(8)
    • 41. ENTHALPY
    • 42. The enthalpy of a substance, h, is defined as
    • 43. h=u+pv
    • 44. where u is specific internal energy, kJ/kg.
    • 45. p is pressure, KPa.
    • 46. v is specific volume, m3/kg.
    • 47. It is an extensive property of the system (kJ/kg).
    • 48. Internal energy change is equal to the heat transferred in a constant volume process involving no work other than pdV work. In such a process in a closed stationary system of unit mass of a pure susbstance
    • 49. dQ=du+pdv
    • 50. where Q = Heat transfer, kJ
    • 51. At constant pressure
    • 52. pdv=d(pv)
    • 53. Therefore,
    dQp=du+d(pv)<br /> or, dQ=d(u+pv)<br /> or, dQ=d(h)<br /> Heat transfer at constant pressure increases the enthalpy of a system<br /> For an ideal gas, the enthalpy becomes<br />h=u+RT<br /> Since internal energy of an ideal gas depends only on temperature, the enthalpy of the ideal gas also depends on temperature.<br />h=f(T)<br />Also, total enthalpy is given by H= m h, kJ<br />and H=U+pV<br />where U= internal energy, kJ,<br />V= volume, m3<br />PERPETUAL MOTION MACHINE OF THE FIRST KIND ---PMM1<br />The first law states the general principle of the conservation of energy. Energy is neither created nor destroyed, but only gets transformed from one form to another. There can be no machine which would continuously supply mechanical work without some other form of energy disappearing simultaneously ( As shown in Figure 1). Such a fictitious machine is called a perpetual motion machine of the first kind, or in brief, PMM1. A PMM1 is thus impossible.<br /> The converse of the above statement is also not true, i.e, there can be no machine which would continuously consume work without some other form of energy appearing simultaneously. ( As shown in Figure 2)<br /> STEADY AND UNSTEADY FLOW PROCESS<br />A flow process is said to be steady when the fluid parameters at any point of the control volume remain constant with respect to time; the parameters may, however, be different at different cross-sections of the flow passage. This means that quantities like velocity, pressure, temperature, etc, are functions only of location and do not vary with time. If any one of these parameters is represented by the symbol P, then mathematically a steady flow is defined as ∂P∂t=0 , i.e., the time rate of change of fluid characteristics at a position is zero.<br /> A steady flow process is characterised by the following conditions in a control volume:<br />
    • No change in the mass of fluid in the control volume; mass inflow equals the mass outflow.
    • 54. The fluid is uniform in state, composition and velocity both at entrance and exit of the control volume.
    • 55. The heat and work interactions at the control surface are at a constant rate.
    • 56. The state of fluid at any point is same at all times.
    • 57. No change in chemical composition of the fluid within the control volume; change in the chemical energy is not involved.
    Flow process is unsteady when the conditions vary with respect to time. Unsteadiness refers to changing parameters with the passage of time at a position in the control volume. Symbolically, ∂P∂t≠0 defines unsteady flow process.<br />REVERSIBLE AND IRREVERSIBLE PROCESSES<br /> A reversible process is defined as a process that can be reversed without leaving any trace on the surroundings (Fig. 6–30). That is, both the system and the surroundings are returned to their initial states at the end of the reverse process. This is possible only if the net heat and net work exchange between the system and the surroundings is zero for the combined (original and reverse) process. Processes that are not reversible are called irreversible processes.<br />29051251104265 It should be pointed out that a system can be restored to its initial state following a process, regardless of whether the process is reversible or irreversible. But for reversible processes, this restoration is made without leaving any net change on the surroundings, whereas for irreversible processes, the surroundings usually do some work on the system and therefore does not return to their original state. <br /> Reversible processes actually do not occur in nature. They are merely idealizations of actual processes. Reversible processes can be approximated by actual devices, but they can never be achieved. That is, all the processes occurring in nature are irreversible. But, there are some reasons because of which we study reversible process. There are two reasons. First, they are easy to analyze, since a system passes through a series of equilibrium states during a reversible process; second, they serve as idealized models to which actual processes can be compared.<br />Engineers are interested in reversible processes because work-producing devices such as car engines and gas or steam turbines deliver the most work, and work-consuming devices such as compressors, fans, and pumps consume the least work when reversible processes are used instead of irreversible ones.<br /> Reversible processes can be viewed as theoretical limits for the corresponding irreversible ones. Some processes are more irreversible than others. We may never be able to have a reversible process, but we can certainly approach it. The more closely we approximate a reversible process, the more work delivered by a work-producing device or the less work required by a work-consuming device. <br />

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