# ENGR 2213 Thermodynamics

Mechanics

Oct 27, 2013 (4 years and 6 months ago)

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ENGR 2213 Thermodynamics

F. C. Lai

School of Aerospace and Mechanical

Engineering

University of Oklahoma

Second Law of Thermodynamics

Any device that violates either the first or the second

law of thermodynamics is called a perpetual
-
motion

machine.

Perpetual
-
Motion Machines

Perpetual
-
Motion Machines of the First Kind

Devices that violates the first law of thermodynamics.

Perpetual
-
Motion Machines of the Second Kind

Devices that violates the second law of

thermodynamics.

Second Law of Thermodynamics

Perpetual
-
Motion Machines of the First Kind

Turbine

Boiler

Condenser

Pump

Generator

Q
L

W

Second Law of Thermodynamics

Perpetual
-
Motion Machines of the Second Kind

Turbine

Boiler

Condenser

Pump

Q
OUT

Second Law of Thermodynamics

Perpetual
-
Motion Machines of the Second Kind

Turbine

Boiler

Pump

W

Q
IN

Second Law of Thermodynamics

Cold Fusion

Second Law of Thermodynamics

Cold Fusion

http://www.ncas.org/erab/index.html

Second Law of Thermodynamics

Reversible Process

A process which can be reversed without

leaving any trace on the surroundings.

Reversible processes actually do not occur in

nature. They are merely idealizations of actual

processes.

Both the system and the surroundings are

returned to their initial states at the end of the

reversed process.

Second Law of Thermodynamics

Irreversibilities

The factors that cause a process to be irreversible.

Friction

Unrestrained Expansion

Mixing of Two Gases

Heat Transfer across a Finite Temperature

Difference

Electrical Resistance

Chemical Reactions

Second Law of Thermodynamics

Cycles that consist entirely of reversible processes.

Carnot Cycle

the best known reversible cycle.

Reversible Cycles

proposed in 1824 by French engineer Sadi

Carnot.

composed of four reversible processes, two

Second Law of Thermodynamics

Carnot Power Cycle

1. Reversible isothermal expansion (1
-
2).

-
3).

3. Reversible isothermal compression (3
-
4).

-
1).

p

v

1

4

3

2

Q
H

Q
L

W
net

Second Law of Thermodynamics

Carnot Refrigeration Cycle

-
2).

2. Reversible isothermal expansion (2
-
3).

-
4).

4. Reversible isothermal compression (4
-
1).

p

v

1

2

3

4

Q
L

Q
H

W
net

Second Law of Thermodynamics

Carnot Principles

1.
The efficiency of an irreversible heat engine is

always less than that of a reversible one

operating between the same two reservoirs.

2.
The efficiencies of all reversible heat engines

operating between the same two reservoirs

are the same.

A violation of either statement results in the

Violation of the second law of thermodynamics.

Proof of the First Carnot Principle

High
-
temperature Reservoir at T
H

Low
-
temperature Reservoir at T
L

Q
H

Q
L, Rev

W
Irr

Rev

HE

Irrev

HE

Q
H

Q
L, Irr

W
Rev

W
Irr

> W
Rev

Q
L, Irr

< Q
L, Rev

Assume
η
Irr

>
η
Rev

Proof of the First Carnot Principle

High
-
temperature Reservoir at T
H

Low
-
temperature Reservoir at T
L

Q
H

Q
L, Rev

W
Irr

Rev

Ref

Irrev

HE

Q
H

Q
L,Rev

Q
L, Irr

Irrev Rev

HE Ref

Q
L, Irr

W
Irr

-

W
Rev

Second Law of Thermodynamics

Carnot Principles

2.
The efficiencies of all reversible heat engines

operating between the same two reservoirs

are the same.

The efficiency of a reversible engine is

independent of the working fluid employed and

its properties, the way the cycle is executed, or

the type of reversible engine used.

Second Law of Thermodynamics

η

= f(Q
H
, Q
L
)

Since the energy reservoirs are characterized by

their temperatures,

η

= f(T
H
, T
L
)

Reservoir T
1

Reservoir T
3

Reservoir T
2

A

B

C

A:

B:

C:

Second Law of Thermodynamics

f(T
1
, T
3
) = f(T
1
, T
2
) f(T
2
, T
3
)

What kind of function f would be?

Second Law of Thermodynamics

What kind of function
Φ

would be?

Several functions are possible, and the choice

is completely arbitrary.

Lord Kevin first propose that
Φ
(T) = T.

This equation partially defines the absolute

temperature.

Second Law of Thermodynamics

Efficiency of a Heat Engine

The efficiency of Carnot heat engine is the highest

efficiency a heat engine operating between the two

reservoirs at temperature T
H

and T
L

can have.

Carnot Heat Engines

Second Law of Thermodynamics

Efficiency of a Heat Engine

Maximize the Efficiency of a Real Engine

η
th

<
η
th, rev

=
η
th, rev

>
η
th, rev

Irreversible heat engines

Reversible heat engines

Impossible heat engines

Supply heat at the highest possible temperature

Reject heat at the lowest possible temperature

Example 1

0.5 kg of air undergoes a Carnot cycle with
η

= 0.5.

Given the initial pressure p
1

= 700 kPa, initial

volume V
1

= 0.12 m
3

and heat transfer during the

isothermal expansion process Q
12

= 40 kJ, Find

(a)

the highest and the lowest temperatures in the

cycle.

(b) the amount of heat rejection.

(c) work in each process.

1

2

3

4

p

v

Example 1 (continued)

T
L

= 292.7 K

Carnot cycle

Example 1 (continued)

Q
L

= 20 kJ

Carnot cycle

Process 1
-
2

T
1

= T
2

Δ
U
12

= Q
12

W
12

W
12

= Q
12

= 40 kJ

Process 2
-
3

Q
23

= 0

Δ
U
23

= Q
23

W
23

Example 1 (continued)

Process 3
-
4

T
3

= T
4

Δ
U
34

= Q
34

W
34

W
34

= Q
34

=
-
20 kJ

Process 4
-
1

Q
41

= 0

Δ
U
41

= Q
41

W
41

W
23

= m(u
2

u
3
)

W
41

= m(u
4

u
1
)

= 0.5(423.7

208.8) = 107.5 kJ

= 0.5(208.8

423.7) =
-
107.5 kJ