# Thermodynamic cycles

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## Thermodynamic cycles

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𝑟𝑒𝑣

H

H

C

C

C

H

𝑟𝑒𝑣

𝑟𝑒𝑣

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3

𝐶

𝑟𝑒𝑣

H

C

𝐻

𝑟𝑒𝑣

TH TC

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4

rev

H

C

C

H

TC TH

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𝑛𝑒𝑡

𝐻

𝐶

𝑟𝑒𝑣

H

H

C

C

C

H

TC TH

𝑟𝑒𝑣

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6

𝐻

𝐶

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H

7

𝐻

### at P

H

𝑞𝐶 at PC

William JM Rankine (1820 –1872)

http://en.wikipedia.org/wiki/Rankine_cycle

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𝑛𝑒𝑡

𝐻

𝑛𝑒𝑡

𝐻

8

𝐻

𝑛𝑒𝑡

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9

(1)

(2) (3)

(4)

(1)

(3) (2) (4)

𝜂𝑅𝑎𝑛𝑘𝑖𝑛𝑒 = 𝑤

𝑞𝐻 = 1108

3196 = 34.7%

### 0.1MPa

Saturated water v.f. 0.924 Superheated steam

Subcooled water

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10

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### 0.1MPa

Saturated water v.f. 0.999 Superheated steam

Subcooled water

𝜂𝑅𝑎𝑛𝑘𝑖𝑛𝑒 = 𝑤

𝑞𝐻 = 938.5

3194 = 29.4%

(1)

(3) (2) (4)

𝜂𝑅𝑎𝑛𝑘𝑖𝑛𝑒 = 𝑤

𝑞𝐻 = 1108

3196 = 34.7%

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12

𝐻

H

𝑞𝐶 at PC

𝑞𝐻

𝑤𝑜𝑢𝑡

𝑞𝐶

𝑤𝑖𝑛

Carnot cycle

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### • How does the temperature of gas change when it is forced through a valve or porous plug while kept insulated so that no heat is exchanged with the environment?

13 JP Joule

(1818-1889) W Thomson (Lord Kelvin)

(1824-1907)

𝑃1, 𝑇1 𝑃2, 𝑇2

(throttling process or Joule–Thomson process)

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𝑑𝑈

𝑑𝑡

𝑠

𝑖𝑛

𝑖

𝑖

𝑜𝑢𝑡

𝑜

𝑜

1

1

2

2

1

2

### (isenthalpic)

P1, T1, V1, H1 P2, T2, V2, H2

𝑚1 𝑚ሶ2

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15

ሶ𝑄

(Cold:0~4℃)

(Hot:15~30 ℃)

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### • Carnot cycle

16

𝑄𝐻

𝑄𝐶

𝑊𝑖𝑛

𝑊𝑜𝑢𝑡 𝑊𝑠

Boiler Condenser

Turbine

Pump

Compressor

Evaporator (heater) 𝑄𝐶

𝑄𝐻

Expander or valve Condenser

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17

ሶ𝑄 ሶ𝑄

(Cold)

(Very Cold)

(hot)

(cold vapor)

High P Low P

Low P

Compressor

High P

(Very hot)

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### Condenser Evaporator

ሶ𝑄 ሶ𝑄

ሶ𝑄

ሶ𝑄

ሶ𝑊 High T

High P Vapor

V. Low T Low P Liquid

Low T Low P Vapor

### Condenser Evaporator

ሶ𝑄 ሶ𝑄

ሶ𝑊

High T High P Vapor

Low T High P Liquid V. Low T

Low P Liquid

Low T Low P Vapor

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### • R134a (Refrigerant 134a)

19

1,1,1,2-Tetrafluoroethane Boiling point of −26.3 °C at 1 atm

### Evaporator

ሶ𝑄𝑒𝑣𝑎𝑝 ሶ𝑄𝑐𝑜𝑛𝑑

ሶ𝑊

High T (70℃) High P (10bar) Vapor

Low T (30℃) High P (10bar) Liquid

V. Low T(-20℃) Low P (1.5bar) Liquid/Vapor

Low T (-20℃) Low P (1.5 bar) Saturated

vapor

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### • Superheating (Point 22’)

∴ 𝐶𝑂𝑃 =𝑄𝐶

𝑊𝑐 = 𝑞𝐶 𝑤𝐶

1 2

3 4

1’ 2’

3’

4’ Saturated Liquid Subcooled Liquid

Saturated Vapor

Superheated Vapor

𝑞𝐶

𝑤𝐶

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21

21

### + ∆ℎ

43

Condenser

Evaporator

Compressor Throttling (J-T)

Valve

T2 T3

𝑤𝐶 = ∆ℎ

∆ℎ21

∆ℎ21

∆ℎ43

(T3<T2)

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### • (1895)

23

http://ethesis.nitrkl.ac.in/1466/1/PROCESS_DESIGN.p df

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24

PR

0.72mol/s 3.21

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h

### Cold T

c

Carnot Cycle

Useful energy

Not useful energy (=heat loss) Energy 100

Steam table Internal energy u

Enthalpy h (kJ/kg) P=100kPa, T=200℃ 2658.0 2875.3

P=10MPa, T=325℃ 2610.4 2809.0 50

50

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### – The useful energy based on the surroundings condition as the reference.

26

𝑃0, 𝑇0

𝑃1, 𝑇1 𝑃0, 𝑇2

𝑃0, 𝑇0

𝑤 Still you can produce more work when the temperature T2>T0 !

Carnot Cycle

𝑤𝑐𝑎𝑟𝑛𝑜𝑡 𝑐𝑦𝑐𝑙𝑒

𝑇0

𝑃0, 𝑇0

(no more useful work)

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27

1

1

0

0

1

0

0

1

### − 𝑠

0

Available internal energy

Available PV work Entropy loss or heat loss

(or Available chemical energy)

1

1

0

0

1

0

0

1

0

12

02

1

### − 𝑧

0

= 𝑢1 − 𝑢0 + 𝑃0 𝑣1 − 𝑣0 − 𝑇0 𝑠1 − 𝑠0 + 𝑉ത12

2 + 𝑔𝑧1

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1

1

0

0

1

0

0

1

0

1

0

1

1

1

1

0

0

0

0

1

0

1

0

0

1

0

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SNU NAOE Y. Lim

### Example 3.18

29

Q

𝑚𝑎𝑖𝑟 = 30 kg/min 𝑇1 = 285 K

𝑃1 = 1 bar 𝑃2 = 1 bar

𝑚𝑠𝑡𝑒𝑎𝑚 = 3 kg/min 𝑥3 = 0.9

𝑃3 = 10 bar 𝑥4 = 0.2

𝑃4 = 10 bar Ex 3.18 (exergy loss)

814.4 kJ/min (SRK)

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### Example 3.18

30 From h,s: -794 kJ/min

From ex: -809kJ/min From h s:

From ex: -813/-839

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### Exergy analysis

0

2479.7 910.9

794.4

1568.8 774.4

2479.7 910.9+794.4=1705.3

774.4

Exergy loss through heat exchanger

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### Exergy Analysis

32 http://exergy.se/goran/thesis/paper1/paper1.html

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