Thermodynamics and Heat Transfer for Heat and Refrigeration Technology, Schemes and Mind Maps of Aerodynamics

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THERMODYNAMICS & HEAT TRANSFER  Duration: 36 hours during 12 weeks (4 teaching units/week) - Week 1  8 : Thermodynamics + Week 8 : Midterm Exam - Week 9  12 : Heat Transfer Final Exam 20% 40%  Instructor: HÀ ANH TÙNG – Department of Heat and Refrigeration Technology Instructor: Dr. Tung Ha – Anh HCMUT 2/2016 + Week 4 : Test 1 + Week 10 : Test 2 15% 10% - Week 9  13 : Experimental 15% 1 Objectives of the course  to provide students with knowledge and skills required to apply the basic principles of thermodynamics and heat transfer to perform calculations and explain thermal engineering applications: Ex: - Thermal power plans - Refrigeration and air conditioning systems - Dryers, boilers 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT - Internal combustion engines - Heat exchangers, etc. 2 CHAPTER 3 : Basic Processes of Ideal Gas 3.1 Equation of Ideal Gas 3.2 Specific Heat of Gas 5 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT Part 1: THERMODYNAMICS 3.3 Basic Processes of Ideal Gas 3.1 Equation of Ideal Gas  IDEAL GAS is a hypothetical gas whose molecules occupy negligible space and have no interactions  Real gas can be considered as ideal gas at low pressures and high temperatures 6 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT New words: Ideal gas: Khí lý tưởng Molecules occupy negligible space: Phân tử chiếm thể tích không đáng kể Real gas: Khí thực Low pressures and high temperatures: Áp suất thấp và nhiệt độ cao Equation of Ideal Gas (Clapeyron equation) RTpv  or: GRTpV  in which: - p (N/m2): absolute pressure of the gas - v (m3/kg): specific volume of the gas - V (m3): volume of the gas - T (K): absolute temperature of the gas - G (kg): mass of the gas - R (J/kg.độ) gas constant   8314  R R  is the molecular weight of 1 kmol (Ex:  of O2 is 32 kg, of N2 is 28 kg, etc) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 7 3.2 Specific Heat of Gas  is the heat required to raise the temperature of the unit of a given substance by one degree Celsius  Classification: - Mass - Specific Heat c (kJ/kg/độ) - Volume - Specific Heat c’ (kJ/m3/độ) - kmol – Specific Heat c (kJ/kmol.độ) '4.22 ccc   Relation  We usually use 2 types: cp, cp (at constant pressure); cv, cv (at constant volume) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 10 kmol - Specific Heat of gases (kcal/kmol.độ)  Note: 1 kcal = 4.186 kJ Types of gas kcal/kmol.độ k = cp/cv cv cp Gas of 1 atom (Monatomic gas) 3 5 1.6 Gas of 2 atoms (O2, N2, Air ...) 5 7 1.4 Gas of 3 or more than 3 atoms (CO2, NH3, …) 7 9 1.3 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 11 kmol – Specific Heat of gas  Ex: - O2: cp= 29.3  cp= cp/ = 29.3/32 = 0.9156 kJ/kg.độ - CO2: cp= 37.7  cp= cp/ = 37.7/44 = 0.857 kJ/kg.độ - AIR: cp (kk) = 0.23 cp (O2) + 0.77 cp (N2) = 1.016 kJ/kg.độ Types of gas kJ/kmol.độ k = cp/cv cv cp Gas of 1 atom (Monatomic gas) 12.6 20.9 1.6 Gas of 2 atoms (O2, N2, Air ...) 20.9 29.3 1.4 Gas of 3 or more than 3 atoms (CO2, NH3, …) 29.3 37.7 1.3 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 12 3.3 Basic Processes of IDEAL GAS 3.3.1 Procedure for calculating a process of Ideal Gas 3.3.2 Isochoric process v = const 3.3.3 Isobaric process p = const 3.3.4 Isothermal process T = const 3.3.5 Adiabatic process Q = 0 3.3.6 Polytropic process pvn = const 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 15 3.3.1 Procedure for calculating a process of Ideal Gas Step 1: outline the ENERGY TRANSFER of the process 111 RTvp  222 RTvp  (u1, i1, s1) (u2, i2, s2) Process 1-2 Q, W ? Step 2: determine: - Known parameters? - Unknown parameters? - Equation of the process ? 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 16 Step 3: Calculation 1/ From the process equation  determine unknown parameters p1, v1, T1 p2, v2, T2 Attention: Ideal Gas  cp=cv + R 2/  1212 TTcuuu v  (kJ/kg)  1212 TTciii p  (kJ/kg) T dq ds  (kJ/kg.K) 3/ Expansion (compression) work of the process  2 1 v v pdvw Technical work of the process:  2 1 p p KT vdpw 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 17 3/ Expansion/compression work of Isochoric process: 0 2 1   v v pdvw 4/ Heat transferred in Isochoric process:   uTTcq v  12 (kJ/kg) 5/ Presentation in p-v and T-s diagram Technical work of Isochoric process:  21 2 1 ppvvdpw p p KT   2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 20 3.3.3 Isobaric process p = const 1/ Equation of Isobaric process: 2 2 1 1 T v T v constp  2/  1212 TTcuuu v  (kJ/kg)  1212 TTciii p  (kJ/kg)              1 2 1 2 lnln v v c T T cs T dTc T dq ds pp p (kJ/kg.K) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 21 3/ Expansion/Compression work of Isobaric process:    1212 2 1 TTRvvppdvw v v   (kJ/kg) 4/ Heat transferred in Isobaric process:   wuiTTcq p  12 (kJ/kg) 5/ Biểu diễn quá trình đẳng áp trên đồ thị công p-v và đồ thị nhiệt T-s Technical work:   2 1 0 p p KT vdpw 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 22 5/ Presentation in p-v and T-s diagram 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 25 3.3.5 Adiabatic process Q = 0 1/ Equation of Adiabatic process: kk k vpvp constpvq 2211 0   Note: v p c c k Adiabatic index ; 1 2 1 1 2 k p p v v        1 2 1 1 1 2 1 2                k k k v v p p T T; 2 1 1 2 k v v p p        2/  12 TTcu v  (kJ/kg)  12 TTci p  (kJ/kg) 1200 sss T dq ds  (kJ/kg.K) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 26 3/ Expansion/Compression work of Adiabatic process:   2 1 2 1 11 v v k k v v v dv vppdvw (kJ/kg)   11 2211 21      k vpvp TT k R w - From definition: - From the 1st law:  210 TTcuwwuq v                                     1 2 111 1 2 11 1 1 1 1 kk v v k vp v v k RT wor:                                        k k k k p p k vp p p k RT w 1 1 211 1 1 21 1 1 1 1 or: * Technical work of Adiabatic process: wkwKT  2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 27 2/ Calculation of the Polytropic exponent n 1 2 2 1 log log v v p p n  2 1 1 2 log log 1 v v T T n  1 2 1 2 log log 1 p p T T n n   or: or: 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 30 3/  12 TTcu v  (kJ/kg)  12 TTci p  (kJ/kg) or from: pdvdTcdq v  1 2 1 2 lnln v v R T T cs v  or from: vdpdTcdq p  1 2 1 2 lnln p p R T T cs p  or from: RdTvdppdv  1 2 1 2 lnln p p c v v cs vp         1 2ln T T cs T dTc T dq ds n (kJ/kg.K) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 31 4/ Expansion/Compression work of Polytropic process:   2 1 2 1 11 v v n n v v v dv vppdvw (kJ/kg) - From definition:                                    1 2 111 1 2 11 1 1 1 1 nn v v n vp v v n RT wor:                                        n n n n p p n vp p p n RT w 1 1 211 1 1 21 1 1 1 1 or:   11 2211 21      n vpvp TT n R w * Technical work of Polytropic process: wnwKT  2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 32 Example: p1= 1 at T1= 20 oC Adiabatic p2= 8 at ?2T ?2v ?w The process is adiabatic, hence: k k p p T T 1 1 2 1 2         2T 222 RTvp  2v   021  TTcw v The system received external work (Air is compressed) 2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 35 Example: Polytropic p1= 1 bar T1= 27 oC 3kg KK p2= 15 bar T2= 227 oC ?n ?2V ?W ?Q The process is polytropic, hence: 1 2 1 2 log log 1 p p T T n n   n 222 GRTVp  2V  21 1 TT n R GGwW    và  12 1 TT n kn cGGqQ v     2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 36 Example: p1= 5 bar t1= 120oC KK t2= 50 oC ?s Polytropic q = 60 kJ/kg Polytropic process:        1 2ln T T cs n determine cn ? kgkJ T q cTcq nn /857.0 12050 60      Từ: KkgkJ T T cs n ./168.0 273120 27350 ln857.0ln 1 2                2/2016 Instructor: Dr. Tung Ha – Anh HCMUT 37