上海交通大学：《热力学 Thermodynamics（I）》课程教学资源（课件讲义）Lecture 29_Carnot Cycle

上游充通大学 SHANGHAI JIAO TONG UNIVERSITY Engineering Thermodynamics I Lecture 29 Chapter 6 The second law of Thermodynamics (Section 6.7-6.11) Spring,2017 强 Prof.,Dr.Yonghua HUANG nna。 http://cc.sjtu.edu.cn/G2S/site/thermo.html 1日

Engineering Thermodynamics I Lecture 29 Spring, 2017 Prof., Dr. Yonghua HUANG Chapter 6 The second law of Thermodynamics (Section 6.7- 6.11) http://cc.sjtu.edu.cn/G2S/site/thermo.html

A cycle exhibits the Carnot efficiency Hot Carnot efficiency of a power cycle: reservoir H Te mmax 1- (Temperatue in Kelvin or Boundary →Weycle=QH-Qc Rankine scale) Cold Carnot cycle,Ericsson cycle, reservoir Stirling cycle,… four internally reversible processes: two adiabatic processes two isothermal processes 3 _TH C 上游充通大 Apr/10,Mon,2017 2 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 2 A cycle exhibits the Carnot efficiency Carnot cycle, Ericsson cycle, Stirling cycle, …. Carnot efficiency of a power cycle: four internally reversible processes: two adiabatic processes + two isothermal processes (Temperatue in Kelvin or Rankine scale)

Carnot cycle and processes (1)+(2) Energy source atTH 2 TH=const. (2)→(3) net,out TL=const. uone nsul 个0 3 (4)4一(3) Process 1-2:Reversible Isothermal Expansion (TH). Energy sink s50 at TL Process 2-3:Reversible Adiabatic Expansion(TH>Tc) QL Process 3-4:Reversible Isothermal Compression (T) (1)←(4) Process 4-1:Reversible Adiabatic Compression (Tc>TH) uone nsul T T 上游充通大 Apr/10,Mon,2017 3 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 3 Carnot cycle and processes Process 1-2: Reversible Isothermal Expansion (TH ). Process 2-3: Reversible Adiabatic Expansion (THTC ) Process 3-4: Reversible Isothermal Compression (TL ) Process 4-1: Reversible Adiabatic Compression (TCTH )

Reversibility of the processes Process 1-2&3-4:adiabatically reversible (isotropic) Process 2-3 4-1:Heat transfer TH △I vanishingly small→reversible; (1)+(2) 4 Energy source at TH △T→0 Reservoir TH Tc const.>gas Tconst. 上游充通大学 Apr/10,Mon,2017 4 SHANGHAI JLAO TONG UNIVERSITY

Apr/10, Mon, 2017 4 Reversibility of the processes Process 1–2 & 3-4: adiabatically reversible (isotropic) Process 2–3 & 4-1: Heat transfer ∆T vanishingly small  reversible; Reservoir TH & TC const.  gas T const. ∆T 0

Work on p-v diagram of Carnot cycle Area 1-2-a-b-1:compression work Wcs/m Area 2-3-c-a-2:expansion work WeT/m Area 3-4-d-c-3:expansion work Wes/m Area 4-1-b-d-4:compression work WeT/m “+”0r“”? a d What about the net work of Carnot cycle? How to evaluate the workand heat 上游究通大学 Apr/10,Mon,2017 5 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 5 Work on p-v diagram of Carnot cycle Area 1-2-a-b-1: compression work WcS/m Area 2-3-c-a-2: expansion work WeT/m Area 3-4-d-c-3: expansion work WeS/m Area 4-1-b-d-4: compression work WcT/m a b c d What about the net work of Carnot cycle? How to evaluate the workand heat ? “+” or “-” ?

Work and heat transfer of Carnot Cycle w= If ideal gas: -)0c-) n-1 gcg-) n≠1 W=RTnotln(V3NV2) State 2 q=w State 3 Thot isothermal Thot q=0, W=-Cy AT adiabatic adiabatic q=0, W=Cy AT State 1 isothermal State 4 Tcold W=RTcoldln(VN) Tcold q=w 图 上游充通大 Apr/10,Mon,2017 6 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 6 Work and heat transfer of Carnot Cycle State 2 Thot State 3 Thot State 1 Tcold State 4 Tcold isothermal adiabatic adiabatic isothermal q=0, w=-cV T q=0, w=cV T w= RThotln(V3 /V2 ) q=w w= RTcoldln(V1 /V4 ) q=w If ideal gas:       1 2 1 2 2 1 1 1 1 1 v v R w T T c T T n n n q c T T n              n≠1

How to realize Carnot cycle Not limited to closed system in piston-cylinder also to vapor power plant (boiler,phase change,const.T) Tc/boiler 4 3 _TH pump turbine TH condenser 、 Tc U also charge/discharge capacitor,magnetize/demagnetize paramagnetic substance,.. 上游充通大学 Apr/10,Mon,2017 7 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 7 How to realize Carnot cycle Not limited to closed system in piston-cylinder also to vapor power plant (boiler, phase change, const. T) turbine condenser pump boiler also charge/discharge capacitor, magnetize/ demagnetize paramagnetic substance, …

Reverse Carnot cycles Refrigeration/Heat pump cycle: P Process 1-2:gas expands adiabatically Shaded area:input work until its temperature decreases to Tc. Process 2-3:gas expands isothermally at TH=const. 4 Tc while receiving energy Qc from cold reservoir net.in Process 3-4:gas compressed adiabatically TL=const. until its temperature is TH. OL 3 Process 4-1:gas compressed isothermally at TH while it discharges energy QH to hot reservoir. 图 上游充通大 Apr/10,Mon,2017 8 SHANGHAI JIAO TONG UNIVERSITY

Apr/10, Mon, 2017 8 Reverse Carnot cycles Refrigeration / Heat pump cycle : Process 1–2: gas expands adiabatically until its temperature decreases to TC . Process 2–3: gas expands isothermally at TC while receiving energy QC from cold reservoir Process 3–4: gas compressed adiabatically until its temperature is TH . Process 4–1:gas compressed isothermally at TH while it discharges energy QH to hot reservoir. Shaded area: input work

Homework: Problems:6.82,6.105 Reading: Chap.7.1 上游充通大 Apr/10,Mon,2017 9 SHANGHAI JLAO TONG UNIVERSITY

Apr/10, Mon, 2017 9 Homework: Problems: 6.82, 6.105 Reading: Chap.7.1