上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY Engineering Thermodynamics I Lectures 15 Spring,2017 Prof.,Dr.Yonghua HUANG R几L E http://cc.sjtu.edu.cn/G2S/site/thermo.html 1日G
Engineering Thermodynamics I Lectures 15 Spring, 2017 Prof., Dr. Yonghua HUANG http://cc.sjtu.edu.cn/G2S/site/thermo.html
Polytropic Process Defining a polytropic process of a closed system: 400 300 燃烧结束 sgpr一nogvse ph=cnsn log p 200 点火 Any gas/liquid 100 l=1.30 膨胀 State1→State2: 40 压缩 =1.29 30 20 排气 or 大气 10 8 index 6 In(p2/p) 56810 203040V constant.-o∞~+o∞ n= Exp.observation log V In(v/v2) 上游充通大 Mar/15,Wed,2017 2 SHANGHAI JIAO TONG UNIVERSITY
Mar/15, Wed, 2017 2 Polytropic Process Defining a polytropic process of a closed system: n pV constant constant: -∞ ~ + ∞ State 1State 2: 1 1 2 2 n n pV p V or 2 1 1 2 n p V p V log p Exp. observation log V 2 1 1 2 ln / ln / p p n v v Any gas/liquid log p=-nlogV+c index
Polytropic process Ideal gas Any gas/liquid P (Ideal gas EoS) i.e. py pvz T Ideal gas n-1 only 27 n or P 上游究大学 Mar/15,Wed,2017 3 SHANGHAI JLAO TONG UNIVERSITY
Mar/15, Wed, 2017 3 Polytropic process + Ideal gas 1 1 2 2 1 2 p V p V T T (Ideal gas EoS) 2 2 2 1 1 1 T p V T p V 1 2 2 1 1 n n T p T p 2 1 1 2 n p V p V or Ideal gas only 1 1 1 2 1 1 1 2 1 2 2 n n n n n V V V V V V V V Any gas/liquid 1 2 1 1 2 n T V T V i.e
Four particular cases n=0 p =const. (isobaric process;constant pressure process) n=1 pv =const. (isothermal process;constant temperature process) p"=p2V2” n=K pv*=const. (isentropic process;reversible adiabatic process) For ideal gas:adiabatic index K =k(specific heat ratio) n=士o∞ V=const. (isometric/isochoric process;constant volume process) 上游充通大学 Mar/15,Wed,2017 4 SHANGHAI JLAO TONG UNIVERSITY
Mar/15, Wed, 2017 4 Four particular cases 1 1 2 2 n n pV p V n p 0 const. n pv 1 const. n pv const. n v const. (isobaric process; constant pressure process) (isometric/isochoric process; constant volume process) (isentropic process; reversible adiabatic process) (isothermal process; constant temperature process) For ideal gas: adiabatic index = k (specific heat ratio)
Work of a polytropic process m- w= Vn (constant）V3-"-(constant)）V}-" (n卡1) 1-n (pV)Vg-"-(p,V）V-nt (Any fluids) 1-n 11-n mR(T2-Ti) (ideal gas,n≠I) 1-n or w= (T-T) for unit mass,ideal gas 1-n isothermal [v dv W constant v= V (n=1) (Any fluids) (ideal gas,n 1) or mRT In- w=RTIn for unit mass,ideal gas 上泽通大学 Mar/15,Wed,2017 5 SHANGHAI JIAO TONG UNIVERSITY
Mar/15, Wed, 2017 5 Work of a polytropic process isothermal (Any fluids) (Any fluids) 2 1 1 R T T w n or for unit mass, ideal gas for unit mass, ideal gas 2 1 RT ln v w v or