Topic 3

The second law of thermodynamics

Predict the direction of changes

Contents Spontaneous processes The second law of thermodynamics The Carnot Heat Engine Entropy and Clausius inequality Gibbs and Helmholz energies and their applications

Thermodynamic relationships

State A State B

?

Reactants Products

?

3.1 Spontaneous Processes

The reverse process never happens under the same set of conditions

Process occurring spontaneously in one direction cannot also take place spontaneously in the opposite direction

Irreversible

Changes that occurs without the addition of energy.

Why?

When a change occurs, the total energy of an isolated system remains constant but it is parcelled out in different ways.Can the direction of change is related to the distribution of energy?

The direction of energy transformation The first law of thermodynamics

ΔU=Q+W

Q W

Is it possible?

The second types of perpetual motion machine

It is impossible for a system to undergo a cyclic process whose sole effects are the flow of heat into the system from a cold reservoir and the flow of an equal amount of heat out of the system into a hot reservoir.

-------Clausius statement

3.2 The second law of thermodynamics

Irreversible of heat-work transformation

It is impossible for a system to undergo a cyclic process whose sole effects are the flow of heat into the system from a heat reservior and the performance of an equilivalent amount of work by the system on the surroundings. -------Kelvin-plank statement

Grade of energy

Q low

W high

The molecular interpretation of the irreversibility

Thermal motion & directed motion

Heat work

The direction of spontaneous change lead to more disorderly dispersal of the total energy of the isolated system

3.3 The Carnot heat engine

0UQ Q Q

ch

NICOLAS LEONHARD SADI CARNOT (1796-1832)

Discussion

1 0U 1 1Q W

2

1 11

1ln

2

V

V

VW PdV nRT

V

Q3=-W3=-RT2ln （3

4

V

V）

Q4=0 W4= U =C△ v （ T1-T2 ）

Q2=0 W2= U =C△ v （ T2-T

1 ）

1 3 W W W 2h c

1

( ) ln( )V

nR T TV

Efficiency of the Carnot engine

h c

h h

Q QW

Q Q

)0( c Q

2h c

1

2h

1

( ) ln( )

ln( )

VnR T T

VV

nRTV

or

h c

h

c

h

1TT

T

T

T

Discussion: Approaches to increase the efficiency of engine ? Th=560 T℃ c=40 ℃ η=62%

Th=560 T℃ c=10 ℃ η=66%

Th=660 T℃ c=40 ℃ η=66%

Independent on working substances, depend on Th and Tc

Carnot’s Principle

IRR No heat engine can be more efficient than a reversible heat engine when both engines work between the same pair of temperature TH and TC

η(any engine) ≤η(a reversible engine)

the maximum

Impact on engineering

Give out some other examples.

About the thermodynamic temperature scale

(1 )c hT T

Lord Kelvin

η=1, T=0K

η=0, The triple point of water, T=273.16K

Independent of working substances

Efficiency of refrigerator

Coefficient of performance COP

CH

CL

TT

T

W

QCOP

3.4 The entropy function and Clausius inequality

h c h c

h h h

Q Q T TW

Q Q T

h

c

h

c 11T

T

Q

Q

h

h

c

c

T

Q

T

Q

c h

c h

0QQ

T T

Rudolf Julius Enmanvel Clausius

Heat temperature quotient

State function?

For any reversible process

iR

i i

( ) 0Q

T

R( ) 0Q

T

or

R( )ii i

QS

T

The entropy function

R( ) 0Q

T

1 2

B A

R RA B( ) ( ) 0Q Q

T T

1 2

B B

R RA A( ) ( )Q QT T

Rd ( )Q

ST

B

B A RA( )Q

S S ST

T

dQ is the differential of a state function, defined as entropy S

Unit: J.k-1

The Clausius inequality

h

c

h

chR 1

T

T

T

TT

IR R becase

0h

h

c

c T

Q

T

Qthen

iIR

i i

( ) 0QT

h

c

h

chIR 1

Q

Q

Q

QQ

A

IR,A B RBi

( ) ( ) 0Q Q

T T

A B IR,A Bi

( ) 0Q

ST

B A IR,A Bi

( )Q

S ST

A B R,A Bi

( ) 0Q

ST

A B A Bi

( ) 0Q

ST

dQ

ST

d 0

QS

T

A

IR,A B RBi

( ) ( ) 0Q Q

T T

Clausius inequality

•S is state function, ΔS is independent on path

•S is extensive function

•Molecular interpretation of entropy S=klnΩ

3.4 Entropy S and entropy change

BA SSS

Homeworks:

Y: P56: 1, 2, 3

Preview: A: 4.2-4.4 Y: 2.5; 2.6