西南交通大学：《大学物理》课程教学资源（讲稿，双语）CHAPTER 15 The second Law of Thermodynemics and Entropy

UNIVERSITY PHYSICS I CHAPTER 15 The Second law of Thermodynamics and Entropy Chapter 15 The second law of thermodynamics The zeroth law of thermodynamics The expression of the fundamental experiment fact The first law of thermodynamics The a statement of conservation of energy for pure thermodynamic system The second law of thermodynamics: Why we need the second law of thermodynamics?

1 Chapter 15 The second law of thermodynamics The zeroth law of thermodynamics: The expression of the fundamental experiment fact. The first law of thermodynamics: The a statement of conservation of energy for pure thermodynamic system. The second law of thermodynamics: Why we need the second law of thermodynamics?

815.1 why do some things happen, while others do not? 1. Some examples that can not happen One of the sacred truths of physics is the principle of energy conservation. For instance O A rock does not jump spontaneously up to the top of the cliff; ----violate the Cwe theorem 2 Pizza does not warm itself: ----violate the first law of thermodynamics 3 Water cannot become into ice automatically OA drop of ink spread throughout water never regroup into a drop-shaped clump 815.1 why do some things happen, while others do not? It is not the energy of the system that controls the direction of irreversible processes; it is another property that we introduce in this chapter. 2. What is the irreversible processes The isothermal expansion of an ideal gas: 1→H2"H1=Q= nITin2>0 V2→V1W2=Q2=nRTn<0 result W, +W=0 Reversible Q1+Q2=0

2 §15.1 why do some things happen, while others do not? One of the sacred truths of physics is the principle of energy conservation. 1 A rock does not jump spontaneously up to the top of the cliff;----violate the CWE theorem 2 Pizza does not warm itself; ----violate the first law of thermodynamics 3 Water cannot become into ice automatically; 4A drop of ink spread throughout water never regroup into a drop-shaped clump. For instance: 1. Some examples that can not happen It is not the energy of the system that controls the direction of irreversible processes; it is another property that we introduce in this chapter. §15.1 why do some things happen, while others do not? 2. What is the irreversible processes The isothermal expansion of an ideal gas: 1frictionless, quasi-static V1 →V2 ln 0 1 2 1 = 1 = > V V W Q nRT V2 →V1 ln 0 2 1 2 = 2 = < V V W Q nRT result ： 0 W1 +W2 = Q1 + Q2 = 0 Reversible!

815.1 why do some things happen, while others do not? Lead shot Lead Thermal reservoir Control knob (a) Initial state i b) Final state 815.1 why do some things happen, while others do not? @friction, quasi-static V1→V O,=W,+W=nRTIn-+w >0) 2,=Wi+W,=nRTIn -I+w (0 reversible

3 §15.1 why do some things happen, while others do not? 2friction, quasi-static V1 →V2 Q1 = W1 +W f W f V V = nRT + 1 2 ln (>0) (>0) V2 →V1 Q W +W f = ′ 2 1 W f V V = nRT + 2 1 ln (0) result Q1 + Q2 = 2Wf > 0 Irreversible! ： §15.1 why do some things happen, while others do not?

815.1 why do some things happen, while others do not? @frictionless, not quasi-static 2,=W< Pdv=nRT In Q2|=WP=nRW女 resu ltQ1+Q2=W1+W2<0 The wok done on the system: W2l-W, The heat transfer to the environgiht=o Irreversible! s15.2 heat engines and the second law of thermodynamics 1. Heat engines and refrigerator engines We use the word engine to mean a system such as a gas that performs a closed cycle on P-v diagram. If the cycle is performed clockwise we called it a heat engine: If counterclockwise we called it a refrigerator engine. The function of a heat engine is to transform disordered internal energy into macroscopic work using the heat transfer between reservoirs at different temperatures

4 3frictionless, not quasi-static 1 2 1 1 d ln 2 1 V V Q W P V nRT V ∫V = = ∫ result ： 0 Q1 + Q2 = W1 +W2 < The wok done on the system： W2 −W1 The heat transfer to the environment Q2 −：Q1 Irreversible! §15.1 why do some things happen, while others do not? §15.2 heat engines and the second law of thermodynamics 1. Heat engines and refrigerator engines We use the word engine to mean a system such as a gas that performs a closed cycle on P-V diagram. If the cycle is performed clockwise, we called it a heat engine; If counterclockwise, we called it a refrigerator engine. The function of a heat engine is to transform disordered internal energy into macroscopic work using the heat transfer between reservoirs at different temperatures

s15.2 heat engines and the second law of thermodynamics 2. The efficiency of the heat engines Q W>0 For a cycle: ∠1U=0 total =W=0H -ec s15.2 heat engines and the second law of thermodynamics 的 冷凝器 net 2H-e Q =1 2H 2H 2H

5 2. The efficiency of the heat engines QC TC W For a cycle: Q W QH QC U = = − = total ∆ 0 V P W > 0 §15.2 heat engines and the second law of thermodynamics QH QC W1 W2 H C H H C H Q Q Q Q Q Q W = − − = = 1 net ε §15.2 heat engines and the second law of thermodynamics

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