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Unformatted text preview: VII. Power and Refrigeration Cycles
C. The Carnot Power Cycle for an Ideal Gas 1. Description •12 reversible, isothermal expansion •23 reversible, adiabatic expansion •34 reversible, isothermal compression •41 reversible, adiabatic compression P 1 Q41=0 4 QL T QH 2 Wnet,out TH = constant Q23=0 3 TL = constant v
Lesson 23, Geof Silcox, Chemical Engineering, University of Utah TH 1 s4 = s1 QH 2 s2 = s3 TL 4 QL 3 s VII. Power and Refrigeration Cycles
2. Analysis •12 rev., isothermal expansion v QH = −W1−2 = mRTH ln 2 v1 •23 rev., adiabatic expansion ηth ,rev = Wnet ,out Q =1− L QH QH mRTL ln Q2 −3 = 0
•34 rev., isothermal compression v QL = W3 −4 = mRTL ln 3 v4 •41 rev., adiabatic compression P v3 v4 ηth ,rev = 1 − v mRTH ln 2 v1 1 QH
Q41=0 4 QL 2 Wnet,out TH = constant Q23=0 3 TL = constant v Q4 −1 = 0 Lesson 23, Geof Silcox, Chemical Engineering, University of Utah 1 VII. Power and Refrigeration Cycles
2. Analysis (cont.)
k −1 T3 TL ⎛ v 2 ⎞ = =⎜ ⎟ T2 TH ⎜ v 3 ⎟ ⎝⎠ T4 TL ⎛ v1 ⎞ = =⎜ ⎟ T1 TH ⎜ v 4 ⎟ ⎝⎠ v3 v2 = v 4 v1 p 1 Q41=0 4 QL QH 2 Wnet,out TH = constant Q23=0 3 TL = constant v k −1 This was derived for an ideal gas but applies to all working substances. ηth ,rev v3 T v4 =1− =1 − L v2 TH mRTH ln v1 mRTL ln (618) Lesson 23, Geof Silcox, Chemical Engineering, University of Utah VII. Power and Refrigeration Cycles
D. Gas Power Cycle for Spark Ignition, Internal Combustion Engines (Otto Cycle) 1. Definitions a. top dead center (TDC) b. bottom dead center (BDC) TDC Stroke BDC Lesson 23, Geof Silcox, Chemical Engineering, University of Utah 2 VII. Power and Refrigeration Cycles
1. Definitions (cont.) c. mean effective pressure Wnet ,out = ( mep )(Vmax − Vmin )
d. compression ratio r= Vmax VBDC = Vmin VTDC Lesson 23, Geof Silcox, Chemical Engineering, University of Utah VII. Power and Refrigeration Cycles
2. The Air Standard Otto Cycle. The Otto cycle is used to model two and fourstroke engines. The working fluid is air. 12 Isentropic compression. Flywheel carries piston into cylinder to give win. 23 Isometric heat addition. Combustion of gasoline provides heat addition qin. 34 Isentropic expansion. Hot gas expands against piston to do work wout. 41 Isometric heat removal. In fourstoke engines, hot gases are exhausted (10) and fresh air is drawn in (01). Steps (10) and (01) are not part of the twostroke Otto cycle. 3 P qin 2 0 4 win 1 qout wout TDC BDC v Lesson 23, Geof Silcox, Chemical Engineering, University of Utah 3 VII. Power and Refrigeration Cycles
3. Efficiency of Otto Cycle (Two and FourStroke) a. Otto cycle is closed ηth ,otto = w net ,out qin − qout q = = 1 − out qin qin qin b. heat transfer occurs at constant volume qout = u4 − u1 = Cv (T4 − T1 ) ∴ηth ,otto ⎛T ⎞ T1 ⎜ 4 − 1 ⎟ ⎜T ⎟ T −T ⎠ =1 − 4 1 =1 − ⎝ 1 T3 − T2 ⎛T ⎞ T2 ⎜ 3 − 1 ⎟ ⎜T ⎟ ⎝2 ⎠ qin = u3 − u2 = Cv (T3 − T2 ) 3 P qin 2 0 4 win 1 qout wout Lesson 23, Geof Silcox, Chemical Engineering, University of Utah TDC BDC v VII. Power and Refrigeration Cycles
c. power stroke (34) and compression stroke (12) are isentropic with ⎛T ⎞ T1 ⎜ 4 − 1 ⎟ ⎜T ⎟ v2 = v3 ⎠ ηth ,otto = 1 − ⎝ 1 and ⎛ T3 ⎞ v1 = v 4 T2 ⎜ − 1 ⎟ ⎜T ⎟ ⎝2 ⎠ k −1 k −1 3 ⎛ v3 ⎞ T1 ⎛ v 2 ⎞ T4 wout =⎜ ⎟ =⎜ ⎟ = Then P T2 ⎝ v1 ⎠ T3 ⎝ v4 ⎠ qin ηth ,otto ⎛v ⎞ T =1− 1 =1 − ⎜ 2 ⎟ ⎜v ⎟ T2 ⎝ 1⎠ k −1 =1 − 1 r k −1 (98) 2 0 4 win 1 qout v where k = and r = 1 cv v2
TDC
Lesson 23, Geof Silcox, Chemical Engineering, University of Utah cp BDC v 4 VII. Power and Refrigeration Cycles
d. conclusions for Otto cycle • η increases with increasing compression ratio, r, and k • typical values of r are 7 to 10 • for r = 8 and k = 1.4, ηth,otto = 56.5% • actual efficiencies are 25 to 30% Lesson 23, Geof Silcox, Chemical Engineering, University of Utah 5 ...
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This note was uploaded on 09/02/2010 for the course PHYS 2300 taught by Professor Silcox during the Fall '09 term at Utah.
 Fall '09
 Silcox
 Thermodynamics, Power

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