The Second Law of Thermodynamics

1
Chapter 18

• The Second Law of Thermodynamics

2
Irreversible Processes

• Irreversible Processesalways found to proceed
  in one direction
• Examples
• free expansion of ideal gas
• heat flow (for finite DT) from hot to cold
• friction converts mechanical energy to heat

3
Reversible Processes

• Reverisble processes just an idealization, but
  we can come close
• put system in equilibrium (with itself and its
  surroundings)
• make slow, infinitesimal changes in order to
  reverse a process

4
Heat Engine

• Heat enginetransforms heat into mechanical
  energy, W
• Reservoirs
• hot reservoir at TH
• cold reservoir at TC

5
Heat Engine

• engine absorbs heat QH from hot reservoir
• engine discards heat QC to cold reservoir
• engine does work W

6
Heat Engine

• Working substancematerial in engine undergoing
  the heat transfer
• Cyclic process reuse same substance, return it
  to initial state at end of each cycle

7
Q net heat input

• For each cycle
• heat QH enters engine
• heat QC leaves engine
• net heat in per cycle
• Q QH QC
• QH QC

8
Heat Engine

• cyclic processDU 0 for engine during one
  cycle
• 1st Law Q W DU
• Thus for each cycleQ W

9
Heat Engine

• For each cycleQ QH QC
• So by 1st Law
• W Q QH QC

10
EngineEfficiency

• W QH QC
• Perfect engine QC 0
• All experiments QC gt 0
• Efficiency e
• measures how close an engine gets to QC 0

11
EngineEfficiency
12
Ideal Engine

• limiting behavior of real engines
• engine converts heat to mechanical energy
• recall converting mechanical energy to heat is
  irreversible

13
Ideal Engine

• avoid irreversibility
• carry out engine cycle slowly and with reversible
  heat flow
• the reversibility of heat flow motivates the
  allowed processes

14
Ideal Engine

• For reversible heat flow, there can be no finite
  DT between engine and reservoir
• so during heat transfer we need an isothermal
  process

15
Ideal Engine

• If there is a finite DT between engine and
  reservoir, any heat flow would be irreversible
• So when there is a finite DT we need an adiabatic
  process

16
Ideal Engine

• so we are motivated to consider a cycle with only
  two processes
• isothermal
• adiabatic
• called a Carnot cycle

17
Ideal Engine

• efficiency e ?
• working substance ?
• Well calculate e for substance ideal gas
• Actually, e is independent of the working
  substance

18
Carnot Cycle
19
Example engine internal combustion engine
20

• TH is provided by combustion of air-fuel mixture
• TC is provided by exhaust gases venting to
  outside air

21

• fuel gasoline
• working substance mixture of air and burned
  fuel
• this engine doesnt actually recycle the same
  mixture in each cycle, but we can idealize with
  simple models

22
Problem 18-44
23
Refrigerator

• Refrigeratorlike a heat engine, but operating
  in reverse
• Reservoirs
• hot reservoir at TH
• cold reservoir at TC

24
Refrigerator

• refrigerator absorbs heat QC
• refrigerator discards heat QH
• work W done on refrigerator

25
Refrigerator

• cyclic processDU 0 during one cycle
• 1st Law Q W DU
• Thus for each cycleQ W

26
Refrigerator

• So by 1st Law
• W Q
• QH QC
• W QH QC
• QH QC W

27
Announcements

• Today finish Chapter 18
• Wednesday review
• Thursday no class (office hours
  1230-230)
• HW 6 (Ch. 15) returned at front
• Midterms returned at front (midterm scores
  classweb, solutions E-Res)

28
The Second Law of Thermodynamics
29
2nd Law of Thermodynamics

• Four equivalent approaches, in terms of
• Engines
• Refrigerators
• Carnot Cycle
• Entropy

30
Heat Engine

• engine absorbs heat QH
• engine discards heat QC
• engine does work W
• engine efficiency

31
2nd LawEngines

• There are no perfect engines (real engines have e
  lt 1)
• It is impossible for a system to change heat
  completely into work, with no other change to the
  system taking place

32
2nd Law Engine Version

• If 2nd Law werent true
• ships could move by cooling the ocean
• cars could move by cooling surrounding air

33
Refrigerator

• refrigerator absorbs heat QC
• refrigerator discards heat QH
• work W done on refrigerator

34
2nd Law RefrigeratorVersion

• There are no perfect refrigerators (for real
  refrigerators Wgt 0).
• It is impossible for heat to flow from hot to
  cold with no other change to the system taking
  place

35
Engine and Refrigerator versions of 2nd Law
are equivalent
36
See notes

• (a) If you can build a perfect refrigerator,
  then you can build a perfect engine
• (perfect refrigerator) (real engine) perfect
  engine

37
See notes

• (b) If you can build a perfect engine, then
  you can build a perfect refrigerator
• (perfect engine) (real refrigerator) perfect
  refrigerator

38
Engine Efficiency Revisited

• 2nd LawReal engines have efficiency e lt 1.
• How close can we get to e 1?
• Is there a maximum possible efficiency?
• Yes!

39
Carnot Cycle
40
2nd Law Carnot Cycle Version

• e lt eCarnot
• The efficiency e of a real engine operating
  between temperatures TH and TC can never exceed
  that of a Carnot engine operating between the
  same TH and TC

Proof
41
Problem 18-44, Revisited
42
Defining Entropy
See notes

• For Carnot cycle

43

• Any reversible cycle sum of many Carnot cycles
• For cycle, in limit of infinitesimally close
  isotherms

44
Entropy (S)

• Result for a reversible cycle
• This defines a new state variable, entropy (S)

45

• Entropy measures the disorder of a system
• The more heat dQ you add, the higher the entropy
  increase dS that results
• The smaller the temperature T, the larger the
  entropy increase dS that results

46
Entropy (S)

• For any reversible path from state 1 to 2
• This must also equal DS for an irreversible path
  from 1 to 2, since S is a state variable

Exercises 18-20, 18-26
Example 18-8, Problem 18-50
47

• Example 18-8 Free Expansion of Ideal Gas

48
Entropy (S)

• For any reversible path from state 1 to 2
• This must also equal DS for an irreversible path
  from 1 to 2, since S is a state variable

Exercises 18-20, 18-26
Example 18-8, Problem 18-50
49
2nd Law Entropy Version

• If we consider all systems taking part in a
  process,
• For a reversible process
• DStotal 0
• For an irreversible process
• DStotal gt 0

50
Laws of Thermodynamics

• Law state variable
• Zeroth Law temperature T
• 1st Law DU Q W internal energy U
• 2nd Law entropy S

51
Announcements

• Today finish Chapter 18
• Wednesday review
• Thursday no class (office hours
  1230-230)
• HW 6 (Ch. 15) returned at front
• Midterms returned at front (midterm scores
  classweb, solutions E-Res)