5. The Classical Second Law of Thermodynamics

5.1 Heat Engines and Refrigerators

The first law represents the conservation of energy of the system. However, consider these processes

The forward process (solid arrows) can occur in our experience. The reverse process (dotted arrows) cannot occur intuitively.

Both processes do not violate the first law. Thus, the first law does not indicate the direction of the process (or possibility of the process), but the second law does.

A heat engine is a system that operates in a cycle and performs a net positive work and a net positive heat transfer.

A simple heat engine

QH is the heat transferred from a high temperature body (or a heat source). QL is the heat transferred to a low temperature body (or a heat sink). Thermal efficiency (thermal or th)

)tscosthatenergy(Q

)soughtenergy(W

H

thermal

H

L

H

LH

Q

Q 1

Q

QQ

Typical values of th for heat engines large power plants 35-50 %

gasoline engines 30-35 %

diesel engines 35-40 %

small utility-type engines 20 %

A refrigerator or a heat pump is a system that requires work and transfers heat from a low-temperature body to a high-temperature body.

A simple refrigeration cycle

The efficiency of a refrigerator is expressed in termed of the coefficient of performance ( or COP)

)tscosthatenergy(W

)soughtenergy(Q L

1

Q

Q / 1

QQ

Q

L

H

LH

L

Similar to the heat pump

)tscosthatenergy(W

)soughtenergy(Q H

H

L

LH

H

Q

Q 1 / 1

QQ

Q

Note: a single cycle can be served as a refrigerator and heat pump depending on the objective.

5.2 The Second Law of Thermodynamics The Kelvin-Planck statement: you cannot convert 100% of heat to work. Mathematically, th always < 1.

The Clausius statement: you cannot transfer heat from a “cooler” body to a “hotter” body without adding work. Mathematically, always < .

Note: 1. These two statements have never

been proven. 2. These two statements are equivalent. 3. “Perpetual-motion machine” (PMM)

is any devices that violate either the first and second laws. PMM1 violates the first law (creates energy) and PMM2 violates the second law (100% efficiency engine).

5.3 The Reversible Process A reversible process is a process that once having taken place can be reversed without leaving any trace on the surroundings.

An irreversible process is a process that is not reversible.

5.4 Factors that Render Processes Irreversible

1. Friction 2. Unrestrained expansion 3. Heat transfer through a finite

temperature difference 4. Mixing of two different substances 5. Other factors such as heat loss from

electric power or combustion process.

Note: An internally reversible process: no irreversibility occurs within the system boundaries during the process.

An externally reversible process: no irreversibility occurs outside the system boundaries during the process.

Thus, a process is totally reversible or simple reversible if it involves no irreversibility within the system or its surrounding.

5.5 The Carnot Cycle

The question is raised: if th always < 1, what is th,maximum ? The answer is the best known reversible cycle, namely the Carnot cycle, which composes of four reversible processes: 1. Reversible isothermal expansion:

heat transfer from the sink (TH) 2. Reversible adiabatic expansion:

the working fluid drops from TH to TL Reversible isothermal compress3. ion heat transfer to the source (TL)

4. Reversible adiabatic compression the working fluid rises from TH to TL

A Carnot heat engine can be operateusing the steady-state devices:

d

Note: Since the cycle is totally reversible, if

le ycle.

all processes are reversed, the cycbecomes the Carnot refrigeration c

5.6 Two Propositions regarding the Efficiency of a Carnot Cycle.

rreversible engine is always less than versible one perating

between the same two reservoirs.

ible engines operating

etween the same two reservoirs aree same.

First proposition: the efficiency of an ithat of a re o

Second proposition: the efficiency ofthe reversb th 5.7 The Thermodynamic TemperatureScale

Thermodynamic (or absolute) temperature scale is a temperature scale that is independent of the properties of substance used to measure temperature.

From the second proposition, the efficiency of the Carnot cycle is a function of the reservoir temperature only.

)T,T(1 Q

Q1

Q

W HL

H

L

H

th

For simplicity, this relation is given by

T

TQ HH Q

LL

The efficiency of the Carnot engine

becomes

H

L

H

Lth T

T1

Q

Q1

5.8 The Ideal-Gas Temperature Scale

Consider the ideal-gas Carnot engine

Pdv dTC w u d q vo

dvv

dTC RT

vo

For a reversible isothermal process

34L43L

12H21H v/vlnRT

v/vlnRT q q

q q

For a reversible adiabatic process

41

HT

LT

vo

LT

HT

v/vRln dTT

C

C

Thus,

23vo v/vRln dT

T 0

0

1423 v/ v v/v , and

T

T

v/vlnRT

v/vlnRT

q

q

L

H

34L

12H

L

H

U5.9 Ideal Versus Real Machines For a real V.S. Carnot engine

H

Lideal,th

H

Lactual,th T

T1

Q

Q1

For a real V.S. Carnot refrigerator

LH

Lideal

LH

Lactual TT

T

QQ

Q

For a real V.S. Carnot heat pump

LH

Hideal

LH

Hactual TT

T

QQ

Q