ME 300 Thermodynamics II

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1 ME 300 Thermodynamics II Prof. S. H. Frankel Fall 2006 ME 300 Thermodynamics II 1

2 Week 1 Introduction/Motivation Review Unsteady analysis NEW! ME 300 Thermodynamics II 2

3 Today s Outline Introductions/motivations Review Definitions Cycles and systems First and Second Law Properties and their evaluation Problem solving technique ME 300 Thermodynamics II 3

4 Introductions Instructor: Prof. S. H. Frankel Office: ME 165/Chaffee 125 Office/cell phone: / or Office hours: MWF 11:30-12:30PM in ME 165 or by appt. Research website: Class website: Section website: Textbook: Fundamentals of Engineering Thermodynamics, Moran and Shapiro, 5 th Edition ME 300 Thermodynamics II 4

5 Major topic outline/deliverables Motivation Brief overview of governing equations Advanced 2 nd law analysis Mixtures HVAC theory and applications Combustion Power cycle analysis Reading/HW assignments every class Use of EES software for advanced analysis Three exams and one final exam Syllabus/Course policy ME 300 Thermodynamics II 5

6 Motivation Why study thermodynamics? Important for design and analysis of any device/system that involves interchange between work and heat Key applications related to energy and the environment include steam power plants, gas turbine engines, internal combustion engines, refrigeration, and air-conditioning, etc. What s new this time around? Advanced concepts: unsteady systems, exergy analysis, new applications to HVAC, combustion, more complex cycle analysis and more... ME 300 Thermodynamics II 6

7 Key Definitions Property State Process Cycle Equilibrium and Quasi-Equilibrium process Dimensions/Units ME 300 Thermodynamics II 7

8 Main Focus HIGH TEMP. RESERVOIR, T H HIGH TEMP. RESERVOIR, T H HEAT ENGINE REFRIGE- RATOR/HEAT PUMP LOW TEMP. RESERVOIR, T L LOW TEMP. RESERVOIR, T L ME 300 Thermodynamics II 8

9 Key Cycle Relations First Law Second Law ME 300 Thermodynamics II 9

10 Inside the circle HEAT ENGINE ME 300 Thermodynamics II 10

11 Generic System Inlet 1 Open vs. closed Steady vs. unsteady Outlet 3 Inlet 2 Rigid vs. non-rigid Air etc. vs. phase-change substance System boundary ME 300 Thermodynamics II 11

12 Common Systems Rigid tank Piston-cylinder Steady-flow device Nozzle/Diffuser Compressor/Turbine Heat Exchanger Mixing chamber Throttle ME 300 Thermodynamics II 12

13 These devices are real! ME 300 Thermodynamics II 13

14 Governing Equations - mass dm dt cv ( ρ / υ ) = m m m = da= V A Vn i e av ME 300 Thermodynamics II 14

15 Governing Equations - energy de 2 2 cv = m ( h + V + gz) m ( h + V + gz) + Q W dt 2 2 i i e e cv cv ME 300 Thermodynamics II 15

16 Governing Equations - entropy ds dt cv Q = ms ms + +σ j i i e e cv Tj ME 300 Thermodynamics II 16

17 Governing Equations - all dm dt cv = m m ; ( m = AV / υ) i e 2 2 decv V V = m ( h + + gz) m ( h + + gz) + Q W dt 2 2 i i e e cv cv ds dt cv Q = ms ms + + σ j i i e e cv Tj ME 300 Thermodynamics II 17

18 Special Case: Closed System m sys = const E ( = U + KE+ PE) = Q W sys sys sys Q j Ssys = + Tj σ sys ME 300 Thermodynamics II 18

19 Property Evaluation Pure substance Simple compressible substance Key properties State principle State relations Ideal gas vs. pure substance with phase-change ME 300 Thermodynamics II 19

20 Ideal Gas (IG) Gases at low pressure and high temperature relative to critical point values Low density Neglects volume of molecules Neglects intermolecular forces Equation of state Internal energy and enthalpy only function of temperature; entropy still function of T and P ME 300 Thermodynamics II 20

21 Pure substance with phase change ME 300 Thermodynamics II 21

22 Property Tables Saturated liquid/vapor states (T/P) - quality Superheated vapor Compressed (subcooled) liquid Water, R134a, Ammonia, Propane Specific heats Ideal gas properties of air (A-22) Ideal gas properties of gases (A-23) ME 300 Thermodynamics II 22

23 Tie-in to Governing Equations Recall conservation of energy (1 st law): de 2 2 cv = m i( h + V + gz) i m e( h + V + gz) e + Q cv W cv dt 2 2 Apply to steady, single-inlet, single-outlet adiabatic rigid control volume neglecting PE changes: ME 300 Thermodynamics II 23

24 Evaluating Enthalpy Change ME 300 Thermodynamics II 24

25 Evaluating Entropy Change ME 300 Thermodynamics II 25

26 Problem Solving Method List what you are given List what you are asked to find Draw and label sketch and identify system (open/closed?) List assumptions Identify and fix your states! Identify special processes (Is anything constant?) Develop governing equations Substitute numerical values identifying data source Check units! Examine your answer critically Comment ME 300 Thermodynamics II 26

27 Summary Appreciate intimate connection between your system and the appropriate form of the governing equations Appreciate mathematical and physical meaning of terms in governing equations Evaluation of properties (changes) differs for ideal gas vs. pure/phase change substance Problem solving technique complements thermodynamic knowledge (above) Next time... Examples and unsteady flow ME 300 Thermodynamics II 27

28 Today s Outline Review (continued) - Example Unsteady flow Governing equations Examples ME 300 Thermodynamics II 28

Example 8-77 Liquid water at 200kPa and 20C is heated in a chamber by mixing it with superheated steam at 200kPa and 300C. Liquid water enters the mixing chamber at a rate of 2.

29 Example 8-77 Liquid water at 200kPa and 20C is heated in a chamber by mixing it with superheated steam at 200kPa and 300C. Liquid water enters the mixing chamber at a rate of 2.5kg/s and the chamber is estimated to lose heat to the surroundings at a rate of 600kJ/min. If the mixture leaves the chamber at 200kPa and 60C, determine (a) mass flow rate of superheated steam and (b) rate of entropy production. ME 300 Thermodynamics II 29

30 Example 8-77: Solution ME 300 Thermodynamics II 30

31 Example 8-77: Solution ME 300 Thermodynamics II 31

32 Example 8-77: Solution ME 300 Thermodynamics II 32

33 Unsteady Processes ME 300 Thermodynamics II 33

34 Motivation Unsteady flow processes involve changes within the CV with time Examples include (see next slide): Charging a rigid vessel from supply line Discharging fluid from pressurized vessel Driving a gas turbine with pressurized air stored in a large container Start-up or shutdown of engines, devices, etc. Unsteady processes start and end over some finite time period vs. rate Unsteady flow systems, while usually fixed in space, may involve moving boundaries and hence boundary work ME 300 Thermodynamics II 34

35 Illustrations ME 300 Thermodynamics II 35

36 Uniform Flow/Uniform State Assumption Most unsteady flow processes invoke the uniform-flow assumption: Fluid flow at inlet/exit is uniform and steady Fluid properties do not change with time or position over cross-section e.g. single value suffices Uniform state assumes intensive properties within CV are uniform with position at each instant e.g. slow process ME 300 Thermodynamics II 36

37 Governing Equations - Mass Integrate term by term wrt time from initial state 1 to final state 2... dm dt cv = mi m e ME 300 Thermodynamics II 37

38 Governing Equations - Energy Integrate term by term wrt time from initial state 1 to final state 2... de 2 2 cv = m ( h + V + gz) m ( h + V + gz) + Q W dt 2 2 i i e e cv cv ME 300 Thermodynamics II 38

39 Governing Equations - Entropy Integrate term by term wrt time from initial state 1 to final state 2... ds dt cv Q = ms ms + +σ j i i e e cv Tj ME 300 Thermodynamics II 39

40 Typical simplifications Charging a tank e.g. tank filling Initially evacuated tank Initial mass is zero No mass exiting Discharging a tank e.g. tank empyting Initial mass/state known No mass entering m m i me = mh+ Q W ms = i i Q = ms+ + σ j i i cv Tj ME 300 Thermodynamics II 40

Example 5-12 A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries steam at 1MPa and 300C.

41 Example 5-12 A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries steam at 1MPa and 300C. Now the valve is opened, and steam is allowed to flow slowly into the tank until the pressure reaches 1MPa, at which point the valve is closed. Determine the final temperature of the steam in the tank. ME 300 Thermodynamics II 41

42 Example 5-12 ME 300 Thermodynamics II 42

43 Example 5-12 ME 300 Thermodynamics II 43

44 Example 5-12 ME 300 Thermodynamics II 44

45 Summary Governing equations for unsteady flow processes derived by integrating general equations wrt time Uniform state/flow assumption often employed Besides inlet and exit states, unsteady flow processes require specification or determination of initial and final states Without mass flow, equations reduce to those for closed system, as expected ME 300 Thermodynamics II 45

46 Today s Outline Unsteady flow examples ME 300 Thermodynamics II 46

47 Example 5-135E A 4-ft 3 rigid tank contains saturated refrigerant-134a at 100psia. Initially, 20% of volume is occupied by liquid and rest by vapor. A valve at the top of the tank is now opened, and vapor is allowed to escape slowly from the tank. Heat is transferred to the refrigerant such that the pressure inside the tank remains constant. The valve is closed when the last drop of liquid in the tank is vaporized. Determine the total heat transfer for this process. ME 300 Thermodynamics II 47

48 Example 5-135E ME 300 Thermodynamics II 48

49 Example 5-135E ME 300 Thermodynamics II 49

50 Example 5-135E ME 300 Thermodynamics II 50

51 Example A 0.25m 3 insulated pistoncylinder device initially contains 0.7kg of air at 20C. At this state, the piston is free to move. Now air at 500kPa and 70C is allowed to enter the cylinder from a supply line until the volume increases by 50%. Using constant specific heats at room temperature, determine (a) final temperature, (b) amount of mass that entered, (c) work done, and (d) entropy generation. ME 300 Thermodynamics II 51

52 Example ME 300 Thermodynamics II 52

53 Example ME 300 Thermodynamics II 53

54 Example ME 300 Thermodynamics II 54

55 Summary Unsteady flow problems involve a start ( now ) and an end ( until ) Distinguish between charging (filling) and discharging (empyting) Use proper form of governing equations Invoke uniform state/uniform flow assumption Know your working fluid so you evaluate properties correctly e.g. IG vs. pure substance ME 300 Thermodynamics II 55

Chapter 5. Mass and Energy Analysis of Control Volumes

Chapter 5. Mass and Energy Analysis of Control Volumes Chapter 5 Mass and Energy Analysis of Control Volumes Conservation Principles for Control volumes The conservation of mass and the conservation of energy principles for open systems (or control volumes)