熱力學第二定律 - hsiao-scu / FrontPagehsiaoscu.pbworks.com/w/file/fetch/77892788/lecture-19.… · · 2018-05-09Carnot Efficiency 工作效率 ... temperatures: e取決于高溫(TH)和低溫(TL)

Chapter 19 Lecture

© 2012 Pearson Education, Inc. Slide 19-1

Essential University Physics Richard Wolfson

2nd Edition

The Second Law of Thermodynamics 熱力學第二定律

Slide 19-2 © 2012 Pearson Education, Inc.

In this lecture you’ll learn簡介 •  To explain the second law

of thermodynamics and the limitations it puts on our ability to extract useful work from thermal energy sources熱源, 可作之功

•  To understand the thermodynamics of heat engines, refrigerators, and heat pumps熱機,冷氣機,暖氣機.

•  To describe the concepts of energy quality and entropy 熱與熵


The Second Law of Thermodynamics Ｉ •  The second law of thermodynamics is

fundamentally a statement that systems naturally tend toward more disorganized states.

第二定律的重點在於：任何的物質系統, 自然地趨向於較不次序的狀態. (p,V,T) à (p’,V’,T’)

p

V

而有兩種陳述： Kelvin-Planck statement 針對熱機 Claussius statement 針對冷氣機


The Second Law of Thermodynamics II –  Applied to heat engines, the Kelvin-

Planck statement of the second law says that it’s impossible to construct a perfect heat engine—one that operates in a cycle, extracting heat Q and delivering an equal amount of work.

第一種陳述：完美熱機是不存在的.

熱機：利用一個循環過程往復操作的機器（系統）, 結果是對外界做功.

完美熱機：可將吸的熱完全轉化成為功的熱機.


The Carnot Engine 卡諾引擎 •  A conceptually important heat-engine design is the

Carnot engine, whose cycle consists of two adiabatic and two isothermal steps. 2絕熱+2等溫


•  For a Carnot engine, Qc/Qh = Tc/Th, and the efficiency is如果用的是理想氣體, 則

Carnot Efficiency工作效率 •  The efficiency of an engine, defined as the ratio of work

delivered to heat extracted from the hot reservoir, is

工作效率＝作的功/吸收的熱

eCarnot =

WQh

= 1−Tc

Th

h c c

h h h

1Q Q QWeQ Q Q

−= = = −


等溫過程,

Qh=nRTh ln(VBVA)

Qc=−nRTc ln(VDVC)=nRTc ln(

VCVD

)

Qc

Qh

=TcThln(VC /VD )ln(VB /VA )


卡諾引擎的效率

ThVγ−1B = TcV

γ−1C

ThVAγ−1 = TcVD

γ−1

⇒ (VBVA)γ−1 = (VC

VD)γ−1 or VB

VA=VCVD

⇒Qc

Qh

=TcTh

⇒ e =1− Qc

Qh

=1− TcTh


The Second Law of Thermodynamics III –  Applied to refrigerator, the Clausius

statement of the second law says that it’s impossible to construct a perfect refrigerator—one that operates in a cycle, extracting heat from cooler object to a hotter one without doing any work.

第二種陳述：完美冷氣機是不存在的. 冷氣機：利用一個循環過程往復操作的機器（系統）, 其結果是將熱由低溫環境轉到高溫的環境. 完美冷氣機：不需要做功就能夠其結果是將熱由低溫環境轉到高溫的環境.


Equivalence of the two statements of 2nd Law

•  Statements of Kelvin-Planck and Clausius are equivaltent, one violated will led to violation of another.第一陳述與第二陳述是等價的


Carnot’s Theorem 卡諾定理

•  No other engine operating between the same two temperatures can be more efficient than the Carnot engine.

在同樣的高溫與低溫下操作的引擎, 其效率e不可能大於卡諾引擎同上, 所有可逆引擎的效率e都是一樣的


Proof of Carnot’s Theorem證明卡諾定理 –  And the fact that a reversible engine can also operate as a

refrigerator.

可逆的熱機可以作為冷氣機


Proof of Carnot’s Theorem證明卡諾定理 •  Proof of Carnot’s theorem involves showing that a Carnot

engine combined with a more efficient engine would constitute a perfect heat engine:

•  證明方式是提出反證可得違反(第二定律)第一種陳述的結論.(以下60%的是卡諾引擎)

=


Implications for Energy Technology •  The second law limitations on efficiency show that we can’t

convert thermal energy to mechanical work with 100% efficiency. e=100% 不存在 –  The efficiency depends on the highest and lowest available

temperatures: e取決于高溫(TH)和低溫(TL)的差別 •  The former is set by the limitations of materials. TH=材料 •  The latter is, at minimum, the temperature of the ambient

environment. TL=環境


Implications for Energy Technology – Technologies affected include 影響所及

• Electric power plants發電廠 • Gasoline engines汽油引擎 •  Jet aircraft engines 噴射機引擎

A thermal electric power plant: The most common heat sources are fossil fuel combustion and nuclear fission. Typical efficiencies are 30–45%. 熱發電電廠: 用石化燃料或核燃料, 30~45%的效率


Combined Cycle: a Better Power Plant共生電廠 I •  Gas turbines use hot combustion gases to spin a turbine. 氣體渦輪機使用爆燃氣體推動渦輪發電

–  Jet aircraft engines are common examples.

例如飛機的噴射引擎（是產生推力而非發電) –  Gas turbines have high operating temperatures Th.

這一類渦輪機的高溫很高 –  But they aren’t very efficient because they have high Tc as well.

但是低溫也很高, 所以熱機效率不好

eCarnot =1−TcTh


Combined Cycle: a Better Power Plant共生電廠 II •  Using the exhaust from a gas

turbine to drive a conventional steam cycle produces a more efficient combined cycle power plant.

但是再將高溫廢氣發動蒸汽機, 合併而成的發電廠

–  Combined cycle plants have efficiencies approaching 60%.

可以達到60%的效率 –  They therefore emit fewer pollutants

and greenhouse gases per unit of electrical energy produced.

可以減少污染物與暖室氣體的排放


Refrigerators and Heat Pumps冷暖氣機, 熱幫浦 •  Refrigerators and air conditioners are examples of heat

pumps—devices that transfer energy from cooler to hotter objects.熱幫浦就包括了冷氣機與暖氣幾 –  The Clausius statement of the second

law says that this transfer can’t occur spontaneously, but requires that external work be supplied.完美的冷氣機不存在(第二定律)

–  Heat pumps can be used for both heating and cooling:

•  They exchange energy with the ambient air or, better,主要是與環境空氣交換能量

•  with the ground, whose temperature stays nearly constant at about 10˚C.


•  The coefficient of performance describes the relative amount of work needed:

–  For a refrigerator, “what we want” is cooling:

–  For a winter heat pump, “what we want” is heating:

–  The larger the temperature difference, the lower the COP and the more work that’s needed.

Coefficient of Performance效率係數

COPrefrigerator =QcW

=Qc

Qh −Qc=

TcTh −Tc

What we wantCOPWhat we put in

=

COPheat pump =Qh

W=

Qh

Qh −Qc

=Th

Th −Tc


•  再感受一下右邊的兩張圖: 熱都是從低溫到高溫! 因為有作功, 熱幫浦才能成真


Energy Quality以可使用的觀點來看能量的品質 •  Energy is not all created equal!

–  Since thermal energy can’t be converted to mechanical work or electricity with 100% efficiency, mechanical work and electricity are higher-quality forms of energy.

•  You can convert them to any other form with 100% efficiency.

•  High temperature thermal energy is higher quality than lower temperature energy, since it can run a more efficient heat engine and thus produce more mechanical work.


Entropy 熵Ｉ •  Entropy is a quantitative measure of energy quality. 熵可以量化能量的品質

–  Formally, entropy describes the degree of order or disorder in a system.代表系統的有序性與無序性

–  The lower the entropy, the more ordered the system and the higher the quality of its energy.

系統的熵小, 就越有序, 系統的能量品質就越高 –  The higher the entropy, the more disordered the system

and lower the quality of its energy. 系統的熵大, 就越無序, 系統的能量品質就越低


Entropy熵ＩI –  Mathematically, the change in

entropy ∆S associated with a thermodynamic process between states 1 and 2 is given by

系統的熵值改變可以寫成: –  An increase in entropy results in the system’s losing

some or all of its ability to do work. 系統的熵值增加則系統做功的能力減少

ΔS = dQ

T1

2

∫


An Example: Adiabatic Free Expansion 例子：絕熱自由膨脹Ｉ

•  A gas is confined to one side of a container; the other side is a vacuum.容器裡只半邊有氣體,另一半邊是真空 –  This is a low-entropy state, since the

gas molecules are organized into one side of the container.這是低熵狀態

•  The system could do work, by turning a paddle wheel.

• 開一小孔就可以推動輪子做功

–  But let the gas expand freely into the vacuum.也可以讓氣體自由膨脹到另一半


An Example: Adiabatic Free Expansion ＩＩ

–  But let the gas expand freely into the vacuum.

•  The new state has the same energy…

•  …but it has higher entropy •  …and it’s lost the ability to do

work. –  The entropy increase is

2

1

ln .VS nRV⎛ ⎞

Δ = ⎜ ⎟⎝ ⎠


Proof 證明

•  膨脹的結果, 系統的內能沒有變化（因為無功無熱） •  如系統裡的氣體是理想氣體, 則可等同於等溫過程

(p,V,T)

(p’,V’,T)

ΔS = ΔQT

=−WT

=nRT ln V2 V1( )

T= nR ln V2 V1( )


Isothermal Processes and the Ideal Gas等溫過程, 理想氣體 I

•  An isothermal process takes place at constant temperature. –  One way to achieve this is to keep the

system in thermal contact with a heat reservoir — a much larger system held at constant temperature.

–  The ideal gas law gives P = nRT/V. –  Then, with constant T, the work done is

( )2 2

1 12 1ln

V V

V V

dVW pdV nRT nRT V VV

= − = − = −∫ ∫

注意：如果體積變大, 系統對外(活塞)做功, W為負. 反過來是外界對氣體做功, W為正


For ideal gas


Entropy and the Second Law •  In terms of entropy, the second law reads

The entropy of a closed system cannot decrease.

–  At best, entropy can remain constant. –  But irreversible processes and dissipative forces like

friction invariably lead to entropy increase. •  When the system enlarges to include the entire

universe, the second law reads

The entropy of the universe cannot decrease.

–  Any situation that appears to involve an increase in order and thus a decrease in entropy is always accompanied by a corresponding and greater increase in entropy.


Summary •  The second law of thermodynamics is fundamentally a

statement about the tendency of systems to evolve toward more disordered states. –  The Kelvin-Planck statement of the second law asserts that it’s

impossible to build a perfect heat engine, one that cyclically converts thermal energy into work with 100% efficiency.

•  The maximum efficiency is the Carnot efficiency: eCarnot = 1 – Tc / Th.

–  The Clausius statement says that it’s impossible to build a perfect refrigerator, one whose sole effect is to transfer energy from a cooler to a hotter object.

•  Real refrigerators therefore require mechanical energy input.

–  In its most general statement, the second law says that the entropy of a closed system cannot decrease.

•  Entropy is a measure of disorder: the higher the entropy, the more disorder.

•  High entropy is associated with low-quality energy, and vice versa.


hsiaoscu.pbworks.com


A Stirling Engine

•  External combustion engine


Homework problems

•  13, 17, 27, 33, 41, 47, 57, 61

Chapter 19 Lecture

© 2012 Pearson Education, Inc. Slide 19-34

Essential University Physics Richard Wolfson

2nd Edition

The Second Law of Thermodynamics 請問


Clicker Question 1

•  Which one of the following processes is irreversible? 何者是不可逆過程?

A.  Stirring sugar into coffee B.  Building a house C.  Demolishing a house by removing one piece at a

time D.  Harnessing the energy of falling water to drive

machinery

Slide 19-3


Clicker Question 2 •  A clever engineer decides to increase the

efficiency of a Carnot engine by cooling the low-temperature reservoir using a refrigerator with the maximum possible COP. How will the overall efficiency of this modified engine compare to that of the original engine?

A.  It will be more efficient. B.  It will have the same efficiency. C.  It will be less efficient.


Clicker Question 3

•  Consider a plant using sunlight, carbon dioxide and water to synthesize glucose. How does the entropy of this system change during this process?

一座工廠是用幾樣原料合成一樣產品, 請問這個過程會使得系統的熵如何改變?

A.  The entropy decreases. B.  The entropy remains the same. C.  The entropy increases.


Clicker Question 4

•  Which of the following statements is FALSE?何者為錯？

A.  A heat pump can deliver heat Q into a room while doing work W, where W < Q.

B.  A refrigerator is a heat engine operating in reverse. C.  An air conditioner operates on the same principle as

a refrigerator. D.  All Carnot engines operating between temperatures

Th and Tc have the same efficiency. E.  The coefficient of performance of a refrigerator is

between 0 and 1.


Clicker Question 5

•  Which of the following statements is TRUE?何者為對？

A.  The second law of thermodynamics is a direct consequence of the first law of thermodynamics.

B.  It is possible to convert work completely into heat. C.  It is impossible to transfer heat from a cooler body to

a hotter body. D.  As water turns into ice in a freezer, its entropy has

increased.


Clicker Question 6

•  Suppose a Carnot refrigerator has a COP of 2.0, what would be its efficiency when operated as an engine?請問….?

A.  1/5 B.  1/3 C.  1/2 D.  2/3 E.  3/5


Clicker Question 7

•  A certain engine extracts 1000 J of heat from a hot temperature reservoir and discharges 800 J of heat to a cold temperature reservoir. What is the efficiency of this engine?請問….?

A.  80% B.  75% C.  40% D.  25% E.  20%

Documents

熱力學第二定律 - hsiao-scu / FrontPagehsiaoscu.pbworks.com/w/file/fetch/77892788/lecture-19.… · · 2018-05-09Carnot Efficiency 工作效率 ... temperatures: e取決于高溫(TH)和低溫(TL)