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## UNIT-I

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**VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITYAERO ENGINEERING**THERMODYNAMICSSEM:III YEAR:IIPREPARED BYMr.B.NarendhiranDEPARTMENT OF AERONAUTICALASSISTANT PROFESSOR**Thermodynamic Systems, States and Processes**Objectives are to: • define thermodynamics systems and states of systems • explain how processes affect such systems • apply the above thermodynamic terms and ideas to the laws of thermodynamics**Internal Energy of a Classical ideal gas**• “Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium. At room temperature, for most gases: • monatomic gas (He, Ne, Ar, …) • 3 translational modes (x, y, z) diatomic molecules (N2, O2, CO, …) 3 translational modes (x, y, z) + 2 rotational modes (wx, wy)**Internal Energy of a Gas**A pressurized gas bottle (V = 0.05 m3), contains helium gas (an ideal monatomic gas) at a pressure p = 1×107 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?**WORK done by the system on the environment**Changing the Internal Energy • Uis a “state” function --- depends uniquely on the state of the system in terms of p, V, T etc. • (e.g. For a classical ideal gas, U = NkT) • There are two ways to change the internal energy of a system: Wby = -Won HEAT is the transfer of thermal energy into the system from the surroundings Q Thermal reservoir Work and Heat are process energies, not state functions.**Increase in volume, dV**+dV Positive Work (Work is done by the gas) -dV Negative Work (Work is done on the gas) Work Done by An Expanding Gas The expands slowly enough to maintain thermodynamic equilibrium.**+dV Positive Work (Work is**done by the gas) -dV Negative Work (Work is done on the gas) A Historical Convention Energy leaves the system and goes to the environment. Energy enters the system from the environment.**Total Work Done**To evaluate the integral, we must know how the pressure depends (functionally) on the volume.**Work depends on the path**taken in “PV space.” The precise path serves to describe the kind of process that took place. Pressure as a Function of Volume Work is the area under the curve of a PV-diagram.**Different Thermodynamic Paths**The work done depends on the initial and final states and the path taken between these states.**p**p p V V V Work done by a Gas • When a gas expands, it does work on its environment • Consider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is: • We generally assume quasi-static processes (slow enough that p and T are well defined at all times): This is just the area under the p-V curve dx dWby = F dx = pA dx = p (A dx)= p dV Note that the amount of work needed to take the system from one state to another is not unique! It dependson the path taken.**Up to mid-1800’s heat was considered a substance -- a**“caloric fluid” that could be stored in an object and transferred between objects. After 1850, kinetic theory. • A more recent and still common misconception is that heat is the quantity of thermal energy in an object. • The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir … (like cash transfers into and out of your bank account) Q U What is Heat? • Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system • Sign of Q : Q > 0 system gains thermal energy • Q < 0 system loses thermal energy**An Extraordinary Fact**The work done depends on the initial and final states and the path taken between these states. BUT, the quantity Q - W does not depend on the path taken; it depends only on the initial and final states. Only Q - W has this property. Q, W, Q + W, Q - 2W, etc. do not. So we give Q - W a name: the internal energy.**The First Law of Thermodynamics (FLT)**-- Heat and work are forms of energy transfer and energy is conserved. U = Q + Won change in total internal energy work done on the system heat added to system State Function Process Functions or U = Q - Wby**1st Law of Thermodynamics**• statement of energy conservation for a thermodynamic system • internal energy U is a state variable • W, Q process dependent**The First Law of Thermodynamics**What this means: The internal energy of a system tends to increase if energy is added via heat (Q) and decrease via work (W) done by the system. . . . and increase via work (W) done on the system.**Isoprocesses**• apply 1st law of thermodynamics to closed system of an ideal gas • isoprocess is one in which one of the thermodynamic (state) variables are kept constant • use pV diagram to visualise process**Isobaric Process**• process in which pressure is kept constant**Isochoric Process**• process in which volume is kept constant**Isothermal Process**• process in which temperature is held constant**Thermodynamic processes of an ideal gas( FLT: DU = Q - Wby**) 2 p Q Q 1 Temperature changes FLT: V p • Isobaric (constantpressure) 1 2 p FLT: Temperature and volume change V • Isochoric (constant volume)**1**2 p Q Thermal Reservoir T FLT: V Volume and pressure change ( FLT: DU = Q - Wby ) • Isothermal (constant temperature)**The First Law Of Thermodynamics**§2-1.The central point of first law §2-2. Internal energy and total energy §2-3.The equation of the first law §2-4.The first law for closed system §2-5.The first law for open system §2-6.Application of the energy equation**§2-1.The central point of first law**1.Expression In a cyclic process, the algebraic sum of the work transfers is proportional to the algebraic sum of the heat transfers. Energy can be neither created nor destroyed; it can only change forms. The first law of thermodynamics is simply a statement of energy principle.**§2-1.The central point of first law**2.Central point The energy conservation law is used to conservation between work and heat. Perpetual motion machines of the first kind.(PMM1) Heat: see chapter 1; Work: see chapter 1;**§2-2.Internal Energy**1.Definition: Internal energy is all kinds of micro-energy in system. 2. Internal energy is property It include: • Kinetic energy of molecule (translational kinetic, vibration, rotational energy) • Potential energy • Chemical energy • Nuclear energy**§2-2.Internal Energy**3.The symbol u: specific internal energy, unit –J/kg, kJ/kg ; U: total internal energy, unit – J, kJ; 4.Total energy of system E=Ek+Ep+U Ek=mcf2/2 Ep=mgz ΔE=ΔEk+ΔEp+ΔU per unit mass: e=ek+ep+u Δe=Δek+Δep+Δu**§2-3. The equation of the first law**1. The equation ( inlet energy of system) – (outlet energy of system) = (the change of the total energy of the system) Ein-Eout=ΔEsystem**Q**W §2-4.The first law in closed system 1. The equation Ein-Eout=ΔEsystem**§2-4.The first law in closed system**Q-W=ΔEsystem=ΔU Q=ΔU+W Per unit mass: q= Δu+w dq=du+dw If the process is reversible, then: dq=du+pdv This is the first equation of the first law. Here q, w, Δu is algebraic.**§2-4.The first law in closed system**The only way of the heat change to mechanical energy is expansion of working fluid.**§2-5. The first law in open system**1. Stead flow For stead flow, the following conditions are fulfilled: • The matter of system is flowing steadily, so that the flow rate across any section of the flow has the same value; • The state of the matter at any point remains constant; • Q, W flow remains constant;**§2-5. The first law in open system**2. Flow work Wflow=pfΔs=pV wflow=pv p V**§2-5. The first law in open system**3. 技术功 “ Wt” are expansion work and the change of flow work for open system. 4. 轴功 “ Ws” is “ Wt” and the change of kinetic and potential energy of fluid for open system.**§2-5. The first law in open system**5. Enthalpy for flow fluid energy: U+pV +mcf2/2+mgz H =U+pV unit: J, kJ For Per unit mass: h=u+pv unit: J/kg, kJ/kg**Q**W §2-5. The first law in open system 6. Energy equation for steady flow open system , mcf12/2, mgz1 U1+p1V1 H1 U2+p2V2 H2 , mcf22/2, mgz2**§2-5. The first law in open system**Per unit mass:**§2-5. The first law in open system**If neglect kinetic energy and potential energy , then: If the process is reversible, then: This is the second equation of the first law.**Q**W §2-5. The first law in open system 7. Energy equation for the open system Inlet flows Out flows 1 1 Open system 2 2 …… … … i j**§2-5. The first law in open system**Energy equation for the open system**Q**Wi §2-6. Application of The Energy Equation 1. Engine a). Turbines energy equation: Ein-Eout=Esystem=0 Wi=H2-H1 wi=h2-h1 , mcf12/2, mgz1 =0 U1+p1V1 H1 Q≈0 U2+p2V2 H2 mcf22/2, mgz2 =0**H2**H1 Wt §2-6. Application of The Energy Equation 1. Engine b). Cylinder engine energy equation: Wt=H2-H1+Q=(U+pV) 2-(U+pV) 1 +Q Ek1, Ep1≈0 Q Ek1, Ep1≈0**H2**H1 Wc Q≈0 §2-6. Application of The Energy Equation 2. Compressors Energy equation: Wc=- Wt =H2-H1 Ek1, Ep1≈0 Ek1, Ep1≈0**§2-6. Application of The Energy Equation**3. Mixing chambers Energy equation: m1h1 + m2h2 -m3h3=0 Mixing water: m3h3 hot water: m2h2 Cold water: m1h1**m3h3**m5h5 m２h２ m1h1 m4h4 m6h6 §2-6. Application of The Energy Equation 4. Heat exchangers Energy equation: (m1h1 + m2h2 + m3h3)-(m4h4 + m5h5 + m6h6)= 0**h2**§2-6. Application of The Energy Equation 5. Throttling valves Energy equation: h1 -h2 =0 h1**Unit - II**Air Cycles