lecture 17 heat engines and refrigerators

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Lecture 17 Heat engines and refrigerators.

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Lecture 17 heat engines and refrigerators

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Page 1: Lecture 17   heat engines and refrigerators

Lecture 17Heat engines and

refrigerators.

Page 2: Lecture 17   heat engines and refrigerators

Heat engine

= device with a working substance (eg. gas) that operates in a thermodynamic cycle. In each cycle, the net result is that the system absorbs heat (Q > 0) and does work (W > 0).

Examples:

- Car engine: burns fuel, heats air inside piston. Piston expands, does mechanical work to move car

- Animal: burns “food” to be able to move

Page 3: Lecture 17   heat engines and refrigerators

Hot and cold reservoirs

Stages of the cycle–Absorb heat from hot reservoir (QH)

–Perform mechanical work (W )–Dump excess heat into cold reservoir (QC < 0)

Reservoir = large body whose temperature does not change when it absorbs or releases heat.

Page 4: Lecture 17   heat engines and refrigerators

Energy flow

Working substance in engine completes a cycle, so ΔU = 0:

H C 0Q Q W

H C H CW Q Q Q Q

This relation follows naturally from the diagram (QH “splits”). Draw it every time!

Page 5: Lecture 17   heat engines and refrigerators

Energy flow diagrams

Page 6: Lecture 17   heat engines and refrigerators

Limitations

We are not saying that you can absorb 10 J of heat from a hot source (a burning fuel) and produce 10 J of mechanical work...

You can absorb 10 J of heat from a hot source (a burning fuel) and produce 7 J of mechanical work and release 3 J into a cold source (cooling system).

… so at the end you absorbed 10 J but used (= converted to work) only 7 J.

(We’ll see later that it is impossible to make QH = W, or QC = 0)

Page 7: Lecture 17   heat engines and refrigerators

Efficiency

what you useEffi ciency

what you pay f or

For a heat engine: H

We

Q

Example: A heat engine does 30 J of work and exhausts 70 J by heat transfer. What is the efficiency of the engine?

H

0.3 (or 30%)W

eQ

C C

30 J

70 J 70 J

W

Q Q

H C 100 JQ W Q

0 1e

Page 8: Lecture 17   heat engines and refrigerators

ACT: Two engines

Two engines 1 and 2 with efficiencies e1 and e2 work in series as shown. Let e be the efficiency of the combination. Which of the following is true?

A. e > e1 + e2

B. e = e1 + e2

C. e < e1 + e2

11

1

22

2

We

Q

We

Q

1 2

1

W We

Q

1 2 1 2Q Q W Q 1 2

1 1

Q Q

1 2

1 1

W W

Q Q 1 2

1 2

W W

Q Q

TC

TH

Q3

Q1

Q2

W2

W1e1

e2

Page 9: Lecture 17   heat engines and refrigerators

The Stirling engine

d

a

b

c

DEMO: Stirling engine

1:

isoch

ori

c

1

hot water 100°C

Gas warms up

2: isotherm

2

hot water 100°C

ΔV

Hot gas

3: iso

choric

3

Room temperature 20°C

Gas cools down

4: isotherm

ΔV

Room temperature 20°C

4

Cold gas

Page 10: Lecture 17   heat engines and refrigerators

Internal combustion engines

The heat source (fuel combustion) is inside the engine and mixed with the working substance (air)

Note: No real cold and hot reservoirs.

- Otto (4 stroke gasoline)

- Diesel

Page 11: Lecture 17   heat engines and refrigerators

Otto cycle

Idealization of the four-stroke gasoline engine

StartQC

Page 12: Lecture 17   heat engines and refrigerators

Intake: • mix of air and fuel enter• at patm

• n increase QC

Compression:

Adiabatic compression:• temperature increase• no heat exchange• work done on the gas (small because of small pressure)

QC

Page 13: Lecture 17   heat engines and refrigerators

Combustion: Heating at constant volume• No work

QC

Power stroke:

Adiabatic expansion•Temperature decrease• No heat exchange •Work done by the gas (large because of large pressure)

QC

Page 14: Lecture 17   heat engines and refrigerators

Heat reject:

When piston at the bottom, very fast cooling, i.e. at constant volume• Excess heat absorbed by water jacket• Valve opens Pressure drops to patm

QC

Exhaust:

n decreaseQC

Page 15: Lecture 17   heat engines and refrigerators

Compression ratio

QC

max

min

compression ratioV

rV

1 12 2 1 1

Compression:

T V TV

1

1 2T rV

1

2 1T T r

1 13 3 4 4

Expansion:

T V T V

1

4 3T rV

13 4T T r

Page 16: Lecture 17   heat engines and refrigerators

Efficiency of the Otto cycle

H 3 2

C 1 4

V

V

Q nC T T

Q nC T T

0

0

H C

H H

Q QWe

Q Q

QC

3 2 1 4

3 2

T T T T

T T

12 1

13 4

T T r

T T r

1 14 1 1 4

1 14 1

T r T r T T

T r T r

14 1

14 1

1T T r

T T r

1

11e

r

Page 17: Lecture 17   heat engines and refrigerators

In-class example: Otto’s engine efficiency

Two idealized Otto cycles have a compression ratio of 5 and 10, respectively. What is the ratio of their efficiencies? Take the gas mixture to be a diatomic gas.

A. 1.27

B. 1.33

C. 1.50

D. 1.67

E. 2.00

10?

5

e r

e r

1.4 1

1.4 1

11

10 101.27

15 15

e r

e r

Diatomic gas:

772 1.4

5 52

P

V

RC

CR

Page 18: Lecture 17   heat engines and refrigerators

Why not simply use a higher compression ratio?

• V2 big huge, heavy engine

• V1 small temp. gets too high premature ignition need to use octane in gas to raise combustion temperature

00.10.20.30.40.50.60.70.80.91

1 5 9 13 17

Conmpression Ratio (V2/V1)

Eff

icie

nc

y o

f O

tto

Cy

cle

Monatomic

Diatomic

Nonlinear'

Compression

Page 19: Lecture 17   heat engines and refrigerators

Real four-stroke engine

The Otto cycle is an idealization:• assumes ideal gas• neglects friction, turbulence, loss of heat to walls

For r = 8 and = 1.4 (air), e = 0.56

Realistic cycle of 4-stroke engine

e ~ 0.3

Page 20: Lecture 17   heat engines and refrigerators

Diesel engine

• Intake and compression happen without fuel.

• Fuel is injected after compression, and keeps pressure constant.

• Compression rate r is 15-20

Larger temperatures

Fuel ignites spontaneously

• Ideal efficiency e ~ 0.65-0.70

Page 21: Lecture 17   heat engines and refrigerators

Refrigerators

• Absorb heat from cold reservoir (QC > 0) • Work done on engine (W < 0)

• Dump heat into hot reservoir (QH > 0)

(We want as much QC while paying for the smallest possible W .)

Energy balance:

H C

H C

W Q Q

W Q Q

CQK

W

Coefficient of performance (refrigerator)

0 K

Page 22: Lecture 17   heat engines and refrigerators

Heat pumps

A very efficient way to warm a house: bring heat from the colder outside.

Same energy diagram as refrigerator

Outside of house TC

Inside of house TH

Heat pump Coefficient of performance (heat pump)

HQK

W

This time we are interested in QH :

1 K