ME 311 - Thermodynamics PDF

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Lesson 1 | Problem Solving Technique 1. Problem Statement: In your own words, briefly state the problem, the key information given, and the quantities to be found. 1. Schematic: Draw a realistic sketch of the physical system, choose your system, list the relevant information on the figure, and indicate mass/energy interactions with surroundings.

1. Assumptions and Approximations: State any appropriate assumptions and approximation made to simplify the problem to make it possible to obtain a solution, and assume reasonable data for missing data.

1. Physical Laws: Apply all the relevant basic physical laws and principles, and reduce them to their simplest form by utilizing the assumptions made.

1. Properties: Determine the unknown properties at known states necessary to solve the problem from property relations or table, and list properties separately and indicate sources.

1. Calculations: Substitute known quantities into the simplest relations and perform the calculations to find unknowns, watch units and round results as appropriate.

1. Reasoning, Verification, and Discussion: Check to make sure that the results obtained are reasonable and intuitive, and verify the validity of the questionable

assumptions

Lesson 1 | Energy and Forms of Energy Energy is the ability to cause changes . Thermodynamics deals with change in total energy, not absolute values.

Macroscopic forms of energy:

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System possesses as a whole with respect to some outside reference frame Kinetic Energy ○ Energy that a system possesses as a result of its motion relative to some reference frame: ■ KE=(mV^(2))/2 kJ ke=V^(2)/2 kJ/kg Potential Energy ○ Energy that a system possesses as a result of its elevation in a gravity field: ■ PE=mgz kJ pe=gz kJ/kg

Microscopic forms of energy: ● Energies related to the molecular structure of a system and degree of the molecular activity ● Independent of outside reference frames ● Sensible Energy ○ Associate with kinetic energy of molecules ○ Increase with increasing temperature ● Latent Energy ○ Associate with bonds between molecules - strongest in solid and weakest in gases ○ By adding energy, molecules of solid or liquid break away, turning the substance into a gas ○ Hases are at higher latent energy level that solids, or liquids ● Chemical Energy ○ Associate with atomic bond in a molecule ● Nuclear Energy ○ Associate with strong bonds within nucleus of atom itself

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The sum of sensible and latent energy is called t hermal energy. The sum of microscopic energies is called internal energy and is denoted by U.

Equations: ● Total Energy, E: ○ E = U+KE+PE => U+(mv^(2)/2)+mgz ● Specific total energy, e: ○ e = E/m = U/m +(KE/m) + (PE/m) => u + V^(2)/2 + gz ● Change of total energy, ΔE or Δe ○ ΔE = ΔU + ΔKE + ΔPE ○ Δe = Δu + Δke + Δpe ○ change in energy of stationary closed systems ■ Δ KE = 0 ■ ΔPE = 0 ■ ΔE = ΔU

Lesson 2 | Energy, Energy Transfer, and General Energy Analysis Homework (Due on the 26th): 2-8, 2-10 | 2-17, 2-29 | 2-39, 2-44 ** - Check Diagram in Book

_____________________________________________________________________Week 2 Energy Transfer: ● Transfer of energy during a process ○ Recognized at the system boundary as they cross it ○ Energy gained or lost by a system during a process ○ Closed System: Fixed mass (not able to leave boundary), energy carried by heat & work ● Open System: Energy is carried by mass and energy (heat and work)

Energy Transfer by Heat and Work ● Heat or heat transfer: ○ The form of energy that is transferred between two systems or a system and its surrounding by virtual of a T difference ○ The direction of heat transfer is always from the higher T body to a lower T one **

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TA < TB

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Tb> Tair

Associated with a process, not a particular state **

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Qualifying Heat: ○

The amount of heat transferred during a process from state 1 to state 2: Q12 or

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Q Heat transfer per unit mass: q = Q/m Rate of heat transfer (the amount of heat transferred per unit time): ■

Q and Q = ∫ Qdt from t1 to t2

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For constant: Q = QΔ t = Q(t2-t1)

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Special Process: adiabatic process ** ○ A process during which there is no heat transfer ○ Two ways a process can be adiabatic: ■ The system is well insulated ■ Both the system and surroundings are at the same T

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Work ○ If the energy crossing the boundary of a closed system is not heat (due to temperature difference), it must be work Quantifying work

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Work done during a process from state 1 to state 2 is W12 or W (kJ)

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Work done per unit mass: w = W/m (kJ/kg)

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Work done per unit time is called Power: W and W = ∫ Wdt from t1 to t2 ■

For constant: W = WΔ t = W(t2-t1)

____________________________________________________________ Week 3

Mechanical forms of Work: ●

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A force acting through a distance ** ○ If F is constant, W = Fs (kJ) ○ W = ∫ Fds from 1 to 2 (kJ) There must be a force acting on the boundary of the system The boundary or the entire system as a whole must move ○ Moving boundary work (ch. 4) ○ Shaft work ○ Spring work

Shaft Work: (picture below) ● Energy transfer with a rotating shaft ● For a specified constant torque T, shaft work during n revolution ○ T = Fr > F = T/r

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Wshaft = Fs = (T/r)(2πrn) = 2πnT (kJ)

Spring Work: (picture above) ● When force is applied to a spring, the length of the spring changes ○ ●

Wspring =  Fds from 1 to 2

For linear elastic spring: F = kx  (kN) ○ k = spring constant, kN/m ○ x = is measured from the undisturbed position of the spring (x = 0 when F = 0)

(kJ) Non-mechanical forms of Work: ● Electrical work ○

Done by electrons crossing the system boundary: We = VN ■

V = potential difference or voltage, Volt

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■ N = number of electrical charges, coulombs In rate form: W = VI

______________________________________________________Energy Transfer____

Key Features of Energy Transfer (heat & work) ●

Key Features: ○ energy transfer occurs during a process ○ Associated with a process, not a stake. Unlike energy and internal energy, energy transfer (heat or work) has no meaning at a state ○ Recognized at the boundary of system as they cross the boundaries ○ System possess energy, but not heat or work

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Sign convention ** ○ Heat and work occur in a particular direction:

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Formal sign conventional ○ Q > 0: heat transfer to  a system ○ Q < 0: heat transfer from  a system ○ W > 0: work done by a system ○ W < 0: work done on a system

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Intuitive Approach ○

Qin: heat transfer to a system

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Qout: heat transfer from a system

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Win: work done on a system

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Wout: work done by a system

__________________________________________________________ Part II

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Magnitudes of energy and internal energy depend on the end states

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Point Functions: ○ Depend on initial and final states, not on how a system reaches that state ○ All properties are point functions ○ They have exact differentials ■ dT, dP, dW, dt, du

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Magnitudes of heat and work depend on the end states a well as the path followed during a process between the two end states Path Functions: ○ depend on process path as well as initial and final states ○ heat and work are path functions ○ they have inexact differentials ■ ∂Q and ∂W instead of dQ and dW

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Consider two processes A and B between the initial state 1 and final state 2 3 ○ Process A: Δ Va = ∫ dV = V2 - V1 = 3m ■ ○

WA = ∫ ∂ WA = 8 kJ 3

Process B: Δ Vb = ∫ dV = V2 - V1 = 3m ■

WB = ∫ ∂ WB = 12 kJ

The First Law of Thermodynamics ● The first law (the conservation of energy principle): T  he net change (increase or decrease) in the total energy of the system during a process is equal to the difference between the total energy entering and total energy leaving the system during the process. ●

[Ein - Eout = ΔEsystem] (kJ)

[Total energy entering the system] - [Total energy leaving the system] = [Change in the total energy of system]

Energy Change, ΔEsystem ● Evaluate the energy of the system at the beginning and at the end of the process, and then take their difference: [Energy change] = [Energy at final state] - [Energy at initial state] ○ ○

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[Efinal - Einitial = -=902 - E1 = ΔE  system] (kJ) Energy is point function

For simple compressible systems (in the absence of electric, magnetic, and surface tension effects) ○ ΔE = ΔU +ΔKE + ΔPE ■ ΔU = m(u2-u1) 2 2 ■ ΔKE = 1/2m(V2 - V1 ) ■ ○

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ΔPE = mg(z2-z1)

For stationary systems: ■ ΔKE = 0 ■ ΔPE = 0 ■ ΔE = ΔU

When the initial and final states are specified, the values of specific internal energies u1 and u2 can  be determined from the property tables or thermodynamic property relations.

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Energy Transfer, Ein and Eout ○

Energy gained or lost by a system during a process

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Heat, work, and mass flow

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Closed systems:

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[ Ein - Eout = (Qin - Qout) + (W  in - Wout) ]

Open Systems

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[ Ein - Eout = (Qin - Qout) + (W  in - Wout) + (E  mass,in - Emass, out)]

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Q, W, and Emass are path functions

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Adiabatic process: Q = 0 Process involving no work interactions: W = 0

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Forms of energy balance ○

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General Form: Ein - Eout = ΔEsystem ■

Ein - Eout : net energy transfer by heat, work, and mass

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ΔEsystem : Change in internal, kinetic, potential, etc,. energies

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ΔKE +ΔPE +ΔU = (Qin - Qout) + (W  in - Wout) + (E  mass,in - Emass, out)

Rate form: Ein - Eout = dEsystem

Energy balance closed system ** ○

Processes that involve Q but no W: ΔU = Qin - Qout

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Processes that involve W but no Q: ΔU = Win - Wout

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Processes that involve Q and W simultaneously: ΔU = (Qin - Qout) + (Win - Wout)

      

Lesson 3 | Properties of Pure Substances Homework: 3: 2, 6, 8, 24, 26, 44 Heating processes under constant P ● Heating under 1 atm

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Compressed liquid or subcooled liquid ○ A liquid is not about to vaporize Saturated liquid ○ A liquid is about to vaporize Saturated liquid-vapor mixture ○ Liquid and vapor phases coexist in equilibrium Saturated vapor ○ A vapor is about to condense Superheated vapor ○ A vapor is not about to condense

Heating under higher P - 1MPa

Compressed liquid > Saturated liquid > Saturated liquid-vapor mixture > Saturated vapor > Superheated vapor T = 20C > 179.88C > __ > 179.88C > 300C v (m3/kg) = 0.00099 > 0.001127 > __ > 0.19436 > 0.25799

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Water starts boiling at a higher temperature Specific volume of saturated liquid is larger and specific volume of saturated vapor is smaller - the saturation line is shorter

Saturation temperature and saturation pressure ●

Tsat: at a given P, the T at which a pure substance changes phase

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Psat: at a given T, the P at which a pure substance changes phase

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There is a definite relation between Tsat and P  sat

Critical Point ● The saturation line eventually becomes a point at 22.06 Mpa ● Critical Point: the point at which the saturated liquid and saturated vapor states are identical 3 ○ For water: Pcr = 22.06MPa (217.8 atm), Tcr = 373.95 C, Vcr = 0.003106 m /kg ●

At pressures above the critical pressure, there is no a distinct phase-change process

Two Lines ● Saturated liquid line: a line connects the saturated liquid states ● Saturated vapor line: a line connects the saturated vapor states

Three Regions ● Compressed liquid region ○ A region to the left of the saturated liquid where all the compressed liquid states are located ● Superheated vapor region ○ A region to the right of the saturated vapor line where all the superheated vapor states are located ● Saturated liquid-vapor mixture region (or wet region) ○ A region under the dome where all the states that involve both phases in equilibrium are located

Extending property diagrams to include solid phase ● Solid-liquid and solid-vapor phase change are similar to liquid-vapor phase-change ● Substances can either contract or expand during freezing ● P-V Diagram of a substance that contracts on freezing

New Property: enthalpy ● Defined to facilitate energy analysis of open systems (control volumes) ○ h = u +Pv (kJ/kg) ○ H = U + PV (kJ) ● Latent Heat: the amount of energy absorbed or released during a phase change process ○

Latent heat of vaporization, hfg: liquid to vapor or vapor to liquid

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Latent heat of fusion, Hif: solid to liquid or liquid to solid

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For water at 1 atm:

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hfg = 2256.5 kJ/kg

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hif = 333.7 kJ/kg

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Saturated liquid and saturated vapor ○ Along saturated liquid and vapor lines on T-v or P-v diagrams ○ For water ■ SI: Table A-4 (p. 904) | Table A-5 (p. 906) ■ English System: Table A-4E (p. 954) | Table A-5E (p.956) ○ For Refrigerant R - 134a ■ SI: Table A-11 (p. 916) | Table A-12 (p. 918) ■ English: A-11E (p. 966) | Table A-12E (p. 967)

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Subscripts f,g, and fg: saturated liquid, saturated vapor, and the difference between the saturated liquid and saturated vapor

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Vf = specific volume of saturated liquid

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Vg = specific volume of saturated vapor

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Vfg = difference between Vg and Vf (that is, Vfg = Vf - Vg)

Saturated liquid-vapor mixture ○ properties of a mixture are the average of the properties of saturated liquid and saturated vapor

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Quality: ratio of the mass of vapor to the total mass of the mixture ○

x = mvapor/mtotal = mg/mt

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where, mt = mf + mg

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X has significance for saturated liquid-vapor mixture only; its value varies between 0 and 1 ■ X = 0 for saturated liquid ■ X = 1 for saturated vapor ■ 0 < x < 1 for saturated mixture

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Specific volume vavg of saturated mixture: V = Vf + Vg ■

V = mf > mtVavg = mfvf + mgvg

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Vavg = vf +xvfg

Other Properties:

Superheated Vapor ● Single-phase region: T and P are independent properties ● For water: ○ SI: Table A-6 (p. 908) ○ English System: Table A-6E (p. 958) ● For Refrigerant R-134a: ○ SI: Table A-13 (p. 919) ○ English System: A-13E (p. 968)

Compressed Liquid: ○ Single-phase region: T and P are independent properties ● For water: ○ SI: Table A-7 (p. 912) ○ English System: A-7E (p. 962) ● Compressed liquid properties are relative independent on pressure, but dependent not temperature ○

, Treat compressed liquid as saturated liquid at the given temperature: y ~ y f@T  ■

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y = v, u, or h

At low to moderate pressure and temperature: h ~ h f@T )     +vf@T  (P-Psat@T

The Ideal-Gas Equation of State:

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Equation of state: Equation that relates properties of a substance at equilibrium states, i.e., P, T, and V Ideal-gas equation of state or ideal gas relation ○ Pv = RT or P = R (T/v) ■ P: absolute pressure ■ v: specific volume ■ T: absolute temperature (K or R, never use Celsius or Fahrenheit) ■ R: gas constant

The gas constant R: different for each gas: Table A-1 (p. 898), Table A-1E (p. 948)

Substance

R, kJ/kg*K

Air

0.2870

Argon (Ar)

0.2081

Carbon Dioxide (CO2)

0.1889

Helium (He)

2.0769

Hydrogen (H2)

4.1240

Neon (Ne)

0.4119

Nitrogen (N2)

0.2968

Oxygen (O2)

0.2598

Water (H2O)

0.4615

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Homework: 3: 55,57,62

R = Ru/M Ru : universal gas constant: same for all gasses

● 8.31447 kJ/kmol * K ● 1.98588 Btu/ilbmol*R M : Molar mass (or molecular weight) of the gas: Table A-1, Table A-1E ● The mass of 1kmol in kg ● 1 mole of substance contains Avogadro’s number of molecules (6.023*10^(26) molecules/mole) ● Mass of a system : m = MN (kg) where N is mole number in kmole

Substance

M, kg/kmol

Air

28.97

Argon (Ar)

39.948

Carbon Dioxide (CO2)

44.01

Helium (He)

4.003

Hydrogen (H2)

2.016

Neon (Ne)

20.183

Nitrogen (N2)

28.013

Oxygen (O2)

31.999

Water (H2O)

18.015

Other forms of ideal-gas equation of state: Pv = RT ● V = mv ➤ PV = mRT ●

mR = (MN)R = NRu ➤ PV = NRuT

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V = N‾v ➤ P‾v = RuT

A bar above a property denotes the value on a unit-mole basis Per unit mass

Per unit mole

3 v, m /kg

3 ‾v, m /kmol

u, kJ/kg

‾u, kJ/kmol

h, kJ/kg

‾h, kJ/kmol

For a closed system, the properties od an ideal gas at two different states are related to each other by: ●

PV/T = R ➤ (P1V1)/T1 = (P2V2)/T2

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Isothermal process (T=constant): ○

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Isobaric process (P=constant): ○

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(P1V1)/T1 = (P2V2)/T2 V1/T1 = V2/T2

Isochoric process (v=constant): ○

P1/T1 = P2/T2

Which gases can be treated as ideal gas? ● Approximates P-v-T behavior of real gases at low densities: low P and high T

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Common gases: air, Ar, Co2, He, H2, Ne, N2, O2 ○ Can be treated as ideal gases: Refrigerant vapor in refrigerators

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○ Can’t be treated as ideal gases - the property tables should be used Water vapor ○ can be treated as an ideal gas at P below 10kPa, regardless of its T ○ can’t be treated as ideal gas at higher P, particularly in the vicinity of the critics point and the saturated vapor line - the property tables should be used Compressibility factor ○ Measure deviation of real gases from ideal gases ○ Z = Pv/RT ○ Pv = ZRT ○ Z = V(actual)/V(ideal) where V(ideal) = RT/P The farther away Z is from unity, the more the gas deviates from ideal-...