s15.2 heat engines and the second law of thermodynamics Define the efficiency of the heat engine QH H TThe first law of thermodynamics W(=Q1 does not forbid E=1 C E=1 eH 2H Perfect engine s15.2 heat engines and the second law of thermodynamics 3. The second law of thermodynamics A perfect heat engines(8=1)do not exist. 4. The examples for efficiency of heat engines a) Clausius-Rankine cycle 1→)2dp=0 QH=nC,t2-l) do=0 2→)3d0=0 12P2=73p 6
6 Define the efficiency of the heat engine: QH W ε = Q C The first law of thermodynamics does not forbid ε =1 Perfect engine ε =1 H C H H C Q Q Q Q Q = − − ε = 1 §15.2 heat engines and the second law of thermodynamics 3. The second law of thermodynamics A perfect heat engines (ε =1) do not exist. 4. The examples for efficiency of heat engines (a) Clausius-Rankine cycle 1 → 2 d p = 0 ( ) QH = nCp T2 −T1 2→3 dQ = 0 1 3 1 1 2 2 − − − − = γ γ γ γ T p T p §15.2 heat engines and the second law of thermodynamics
s15.2 heat engines and the second law of thermodynamics 3→4dp=0gc=nC(T4-) 0=0 T =T1p2 E=1 T-7 =1 OHT2 P≠0 E<1 s15.2 heat engines and the second law of thermodynamics (b)Otto cycle
7 3 → 4 d p = 0 ( ) QC = nCp T4 −T3 4 → 1 dQ = 0 1 1 2 1 4 1 − − − − = γ γ γ γ T p T p H C Q Q ε = 1− 2 1 3 4 1 T T T T − − = − γ −γ = − 1 1 2 1 ( ) p p 0 1 Q P2 ≠ ∴ ε < §15.2 heat engines and the second law of thermodynamics (b) Otto cycle QH W QC e b c d Vf Vi V P a §15.2 heat engines and the second law of thermodynamics
s15.2 heat engines and the second law of thermodynamics →d C, (ld-l) e 2c=nc, (T-T) d →e T TV. O b→CTv"=T b E=1 Ratio of compression s15.2 heat engines and the second law of thermodynamics (c) Diesel cycle P b→cQn=mcp(T-T) d→)aQl=nc(T-T) Th V2 2 c b→c T V c→)dTJ"=Tvy 2 P)ab 2-1=Tyr-l 8
8 1 1 1 1 ( ) 1 1 1 − − = − = − = − − − = − r r i f c b d c e b V V T T T T T T α ε f i V V α = Ratio of compression QH W QC a b c d V f Vi V P e §15.2 heat engines and the second law of thermodynamics ( ) ( ) C V e b H V d c Q nc T T Q nc T T = − c →d = − e →b 1 1 1 1 − − − − = = γ γ γ γ f f T V T V T V T V b i c d →e d e i b →c (c) Diesel cycle a d c b V o p V 2 V3 V1 QH QC ( ) ( 1) ( ) 1 1 2 1 3 2 1 2 3 − − = − − V V V V V V γ γ γ ε §15.2 heat engines and the second law of thermodynamics b→c 3 2 V V T T c b = 1 1 2 1 3 1 1 1 − − − − = = γ γ γ γ T V T V T V T V b a d c c→d a→b ( ) ( ) C V d a H P c b Q nc T T Q nc T T = − b →c = − d →a
8 15.3 The Carrnot heat engine and its efficiency 1. Carrnot cycle of ideal gases a→bQ= nrt\ c→d| EcnR Volume b→cTnV=TV d→aTmV=Tl 8 15.3 The Carrnot heat engine and its efficiency 2. The efficiency of carrnot cycle 2H-1o nRTHIn -nRTIn QH nITIn T the efficiency of Carrnot H cycle for ideal gases
9 §15.3 The Carrnot heat engine and its efficiency 1. Carrnot cycle of ideal gases a b H H V V a →b Q = nRT ln d c C C V V c →d |Q |= nRT ln −1 −1 → = r C c r b c THVb T V −1 −1 → = r C d r d a THVa T V d c a b V V V V = H C H H C a b H d c C a b H H H C T T T T T V V nRT V V nRT V V nRT Q Q Q = − − = − = − = 1 ln ln ln | | ε H C T T ε =1− --the efficiency of Carrnot cycle for ideal gases 2. The efficiency of Carrnot cycle §15.3 The Carrnot heat engine and its efficiency
815. 4 refrigerator engines and the second law of thermodynamics 1. The refrigerator engines P O W<0 W total/g 2Hl-ea 2c 0H=e +w T 815.4 refrigerator engines and the second law of thermodynamics Define the coefficient of performance: K H 1 a perfect refrigerator engine is one that has an infinite coefficient of performance. It does not violate the first law of thermodynamics 2. The second law of thermodynamics A perfect refrigerator engines(K-oo) do not exI st 10
10 §15.4 refrigerator engines and the second law of thermodynamics 1. The refrigerator engines QC TC V P W < 0 Q Q W Q W Q Q H C H C = + total = = − Define the coefficient of performance: 1 1 − = − = = C H C H C C Q Q Q Q Q W Q K A perfect refrigerator engine is one that has an infinite coefficient of performance. It does not violate the first law of thermodynamics 2. The second law of thermodynamics A perfect refrigerator engines (K=∞) do not exist. §15.4 refrigerator engines and the second law of thermodynamics