CENG CENG131 131 Lecture Lecture4.4.Second SecondLaw LawofofThermodynamics Thermodynamics(6(6h) h) Learning Objectives: Learning Objectives: (1) (1)Second SecondLaw LawofofThermodynamics Thermodynamics (2) (2)Entropy Entropyand andReversibility Reversibility (3) (3)Entropy EntropyCalculation Calculation (4) (4)Carnot CarnotHeat HeatEngine Engine (5) (5)Carnot CarnotEfficiency Efficiency Learning LearningGuides: Guides: (1) (1)Lecture Lecturehandouts handouts (2) (2)Chapters Chapters55ofofIntroduction IntroductiontotoChemical ChemicalEngineering Engineering Thermodynamics Thermodynamics5th 5thed. ed.(Smith, (Smith,Van VanNess, Ness,Abbott) Abbott)
Second Law of Thermodynamics (1) No apparatus can operate in such a way that the only effect is to convert heat absorbed by a system completely into work done by the system. “This defines the thermodynamic efficiency and is based on the observation that only a portion of available heat could be converted into useful work” (2) No process is possible which consists solely in the transfer of heat from one temperature level to a higher one. “This is based on the observation that heat always flows spontaneously from a higher to a lower temperature” (3) In an isolated system any transformation of energy into heat is irreversible. “This indicates that all types of energy are eventually degraded into heat, i.e., the entropy of the system + surrounding always increase”
http://www.panspermia.org/seconlaw.htm http://www.chem.uci.edu/education/undergrad_pgm/applets/bounce/bounce_explain.htm
Heat Engines
Temperature-Entropy (TS) Diagram of Nitrogen
Th Qh E
W Qc
Tc ⏐W ⏐ = ⏐Qh ⏐ - ⏐Qc ⏐ η = ⏐W ⏐/ ⏐Qh⏐ = (⏐Qh ⏐ - ⏐Qc ⏐)/⏐Qh ⏐
Experimental data are the most accurate source of information on the P-V-T states of a substance. Note: The data includes both liquid and gas phases. http://www.panspermia.org/seconlaw.htm http://www.chem.uci.edu/education/undergrad_pgm/applets/bounce/bounce_explain.htm
Problem 15: Cooling by burning:A carnot heat engine was used to operate a carnot heat pump in a refrigerator unit. The temperature of the surrounding (i.e., room) to which the excess heat is disposed to is constant at 30°C. The heat source for the heat engine is a small boiler burning Towngas fuel. The boiler temperature is fixed at 450°C and could supply 20 BTU of heat per hour.
Heat Pump
Th Qh
Th
E
Th
E
Tc
⏐Qh⏐ = ⏐Qc⏐ + ⏐W⏐ COP = ⏐Qc⏐/ ⏐W⏐ = ⏐Qc⏐/(⏐Qh⏐- ⏐Qc⏐) COP = Tc/(Th-Tc)
http://www.panspermia.org/seconlaw.htm http://www.chem.uci.edu/education/undergrad_pgm/applets/bounce/bounce_explain.htm
E Qc
Qc Tc
Qh
Qh
W
Qc Tc
(a) How much work can be generated by the heat engine assuming reversible process? What is its efficiency and the amount of waste heat generated? (b) What is the entropy change taking the heat engine as the system? (c) What is the maximum amount of heat that can be removed by the heat pump if the temperature of the refrigerator must be maintained at - 4°C ? What is the COP of the heat pump? (d) What is the entropy change taking the heat pump as the system? (e) What is the entropy change for the each systems if a heat transfer gradient of 20°C is needed for efficient operation and but heat engine and heat pump operates at 60% of maximum efficiency ?
Practical Heat Engines Entropy Calculation (a) Steam Power Plants 1) Carnot cycle 2) Rankine cycle
General Systems: Isothermal systems ∆S = Q/T
Qh
Adiabatic systems
2 boiler
∆S = 0 Ideal Gas: ∆S(T,P)
pump
Ws
turbine
1
W
3
s
condenser 4
dS = CpdT/T - RdP/P ∆S(T,V)
Qc
dS = CvdT/T + RdV/V
Carnot
Rankine
∆S(P,V) dS = CvdP/P + CpdV/V
T
T
S http://www.panspermia.org/seconlaw.htm http://www.chem.uci.edu/education/undergrad_pgm/applets/bounce/bounce_explain.htm
S
Pump
Turbine or Expander
Liquid handling device P2 > P1 H2 > H1 steady state operation m2 = m1 = m m2H2 - m1H1 = m(H2-H1) = Ws reversible, isentropic process m2S2 - m1S1 = m(S2-S1) = m∆S12 = 0
Gas handling device P2 < P1 H2 < H1 steady state operation m2 = m1 = m m2H2 - m1H1 = m(H2-H1) = Ws reversible, isentropic process m2S2 - m1S1 = m(S2-S1) = m∆S12 = 0
m2 ,H2 P2
m1,H1 Ws P1
P1 Ws
m1,H1
m2 ,H2 P2
Practical Heat Engines
Practical Heat Engines
(a) Steam Power Plants 1) Carnot cycle
(a) Steam Power Plants 2) Rankine cycle
Qh
Qh 2
2
boiler
boiler turbine
1 pump
W
3
s
Ws
turbine
1 pump
W
3
s
condenser
condenser
4
4
Qc
Qc
Carnot
Rankine
T
T
S
S
Ws
Examination 2 April 27 (10:00 - 13:00) Rm. 3007 Exam Format: Open book and open notes, bring your own ruler (straight-edge), calculator, pencil and pen. Study Guide: 1) Real Gases (1) PVT data (2) Virial equations (3) Generalized compressibility-factor correlation (4) Generalized virial-coefficient correlation (5) Cubic equations of state Lecture note + photocopied text chpt 3 (a) What is the relationship between the various PVT equations? (b) Please sketch the PV diagram for the following processes: 1) isothermal 2) adiabatic for ethylene assuming ideal gas and using Redlich-Kwong equations. (c) Is it always more difficult to compress a Real gas? (d) What general type of gases will have a compressibility factor that is less than 1? And greater than 1? (e) How do you calculate work for ethylene using the Virial coefficient equation? (f) Is it easier to cool ethylene by expansion if it is an ideal gas or a real gas? And why ?
Examination 1 Study Guide: 2) Second Law of Thermodynamics • be able to state the main concept of the second law of Thermodynamics. • be able to calculate the entropy for an ideal gas • be able to analyze a Carnot heat engine and heat pump cycles lecture note + photocopied text chpt.5 (a) What is the main idea behind the second law of Thermodynamics? (b) Which processes for an ideal gas will have the smallest and highest ∆S ? 1) isothermal expansion 2) adiabatic compression 3) isobaric heating 4) isochoric cooling also draw the PV and TS-diagram for each of the processes. (c) How do Carnot heat engine and heat pump differ? (d) If a real gas is used in a carnot heat engine instead of an ideal gas, how will it change the equation for efficiency?
Practical Heat Engines (b) Internal Combustion Engines 1) Otto engine 2) Diesel engine 3) Jet engine
Otto Engine
Efficiency of an Otto Engine
Diesel Engine
Brayton Engine (Jet engine and gas turbine)
Practical Heat Pumps
High T reservoir
Th Qh E
W Qc
Tc Low T reservoir
Problem 18: Practical heat pumps using heat reservoir and low boiling refrigerant to approximate a carnot heat pump. In the figure, Mr. Brown take advantage of the fact that ground temperature rarely change during the year. He knows he can rely on a constant ground temperature of 15 C during the height of summer (Tair = 35 C) and dead of winter (5 C). If a heat loss from the house is 50 kw/day how much power is needed to maintain a constant room temperature of 20 C throughout the year.
Vapor Compression Cycle
3 4 Expander Turbine
2
High T reservoir
Th
1 Qh
E
W
3 4
4
Qc
3
expander
Tc Low T reservoir
1
2
1
2
Coefficient of Performance Vapor Compression Cycle Carnot Heat Pump (Mechanical Engineering) - can be used for heating and cooling 3
(a) when used for cooling: C.O.P. = |QC | / | WS | = TC/(TH-TC) (b) when used for heating: C.O.P. = |QH | / | WS | = TH/(TH-TC)
4
Refrigeration - used mainly for cooling
2 1
(a) Carnot Refrigerator: C.O.P. = |QC | / | WS | = TC/(TH-TC)
3 4
1
4
2
3
1
2
(b) Vapor Compression Cycle 1) use of expander for energy recovery: C.O.P. = |Qevap|/(|Wcompr| - |Wexp|) 2) use of throttle valve: C.O.P. = |Qevap|/|Wcompr|
Compressor
Throttle Valve
Gas handling device P2 > P1 H2 > H1 steady state operation m2 = m1 = m m2H2 - m1H1 = m(H2-H1) = Ws reversible, isentropic process m2S2 - m1S1 = m(S2-S1) = m∆S12 = 0
Liquid handling device P2 > P1 H2 = H1 steady state operation m2 = m1 = m m2H2 - m1H1 = m(H2-H1) = Ws = 0 irreversible process m2S2 - m1S1 = m(S2-S1) = m∆S12 > 0 m1 ,H
m1,H1
P1 P1 Ws
P2 m2 ,H
m2 ,H2 P2
Coefficient of Performance Vapor Compression Cycle 1) use of expander for energy recovery: C.O.P. = |Qevap|/(|Wcompr| - |Wexp|) Qevap = ∆Hevap = H2 - H1 Wcompr = ∆Hcompr = H3 - H2 Wexp = ∆Hexp = H1 - H4 2) use of throttle valve: C.O.P. = |Qevap|/|Wcompr| Qevap = ∆Hevap = H2 - H1 Wcompr = ∆Hcompr = H3 - H2
Problem 19. Expander or turbine are usually expensive and the vapor compression cycle shown below is only used for centralized air conditioner system installed in large commercial buildings. Such refrigeration systems are also found in manufacturing processes that requires low temperature cooling (e.g., distillation of nitrogen from air). The refrigeration cycle shown below uses tetrafluoroethane (HFC-134a) to maintain a process temperature at 10°F, with 70°F water available for cooling the condenser. (a) Sketch the refrigeration cycle in the PH-diagram. (b) Calculate the T, P, ∆H, ∆S, Q, W for each step of the process. (c) Determine the C.O.P. for the vapor compression cycle.
3 4 Expander Turbine
2 1
