SNU NAOE Y. Lim

**Thermodynamic cycles**

SNU NAOE Y. Lim

**Carnot cycle on T-s diagram**

### Temper atur e T

### Entropy s

### 𝛿𝑞

_{𝑟𝑒𝑣}

### = 𝑇𝑑𝑠

### 12 Isothermal Expansion at T

_{H}

### 23 Adiabatic Expansion T

_{H}

### T

_{C}

### 34 Isothermal Compression at T

_{C}

### 41 Adiabatic Compression T

_{C}

### T

_{H}

### Pressur e P

### Volume v

### 𝑑𝑠 = 𝛿𝑞

_{𝑟𝑒𝑣}

### 𝑇

### 𝛿𝑤

_{𝑟𝑒𝑣}

### = −𝑃𝑑𝑣

SNU NAOE Y. Lim

**Carnot cycle on T-s diagram**

3

### T

### Entropy s 𝑞

_{𝐶}

**3** **4**

### 𝛿𝑞

_{𝑟𝑒𝑣}

### = 𝑇𝑑𝑠

### Isothermal (ΔT=0)

### 12 Isothermal Expansion at T

_{H}

### 34 Isothermal Compression at T

_{C}

### T

### Entropy s 𝑞

_{𝐻}

**1** **2**

### 𝛿𝑞

_{𝑟𝑒𝑣}

### = 𝑇𝑑𝑠

T_{H}
T_{C}

### Pressure P

### Volume v

SNU NAOE Y. Lim

**Carnot cycle on T-s diagram**

4

### Adiabatic and reversible isentropic (q

_{rev}

### =0Δs=0)

### 23 Adiabatic Expansion T

_{H}

### T

_{C}

### 41 Adiabatic Compression T

_{C}

### T

_{H}

### T

### Entropy s

**3** **2**

**4** **1**

T_{C}
T_{H}

### Pressure P

### Volume v

SNU NAOE Y. Lim

**Carnot cycle on T-s diagram**

5

### T

### Entropy s

**3** **2**

**4** **1**

### 𝑞

_{𝑛𝑒𝑡}

### = 𝑞

_{𝐻}

### + 𝑞

_{𝐶}

### 𝛿𝑞

_{𝑟𝑒𝑣}

### = 𝑇𝑑𝑠

### 12 Isothermal Expansion at T

_{H}

### 23 Adiabatic Expansion T

_{H}

### T

_{C}

### 34 Isothermal Compression at T

_{C}

### 41 Adiabatic Compression T

_{C}

### T

_{H}

T_{C}
T_{H}

### Pressur e P

### Volume v

### 𝛿𝑤

_{𝑟𝑒𝑣}

### = −𝑃𝑑𝑣

SNU NAOE Y. Lim

**Practical problems of Carnot cycle**

**• 12 boiler: sat. liquid to sat. vapor**

**• 23 turbine: maybe OK but large amount of liquid ** **flowing into the turbine can cause physical damage**

**• 34 condenser: how to stop at 4?**

**• 41 compressor: how to compress L/G mixture?**

6

### T

### Entropy s

**3** **2**

**4** **1**

### 𝑞 = 𝑞

_{𝐻}

### + 𝑞

_{𝐶}

### Liquid

### Vapor

SNU NAOE Y. Lim

**Rankine cycle**

**• 12 Isobaric** **expansion at P**

_{H}**(T change): boiler**

**• 23 Adiabatic expansion: turbine**

**• 34 Isobaric** **and isothermal** **compression:**

**• 41 Adiabatic compression: pump** **(for 100% liquid)**

7

### T

### Entropy s

**3** **2**

**4** **1**

### cooled Sub- Liquid

### Superheate d Vapor

### Saturated Liquid

### Saturated Vapor with

### less liquid 𝑞

_{𝐻}

### at P

_{H}

𝑞_{𝐶} at P_{C}

William JM Rankine (1820 –1872)

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

SNU NAOE Y. Lim

**Efficiency of Rankine cycle**

### • Δ𝑢 _{𝑐𝑦𝑐𝑙𝑒} = 𝑞 _{𝑛𝑒𝑡} + 𝑤 _{𝑛𝑒𝑡}

### • 𝜂 = ^{𝑤}

^{𝑛𝑒𝑡}

### 𝑞

_{𝐻}

### = ^{𝑞}

^{𝑛𝑒𝑡}

### 𝑞

_{𝐻}

8

### T

### Entropy s

**3** **2**

**4** **1**

### 𝑞

_{𝐻}

### T

### Entropy s

**3** **2**

**4** **1**

### 𝑞

_{𝑛𝑒𝑡}

SNU NAOE Y. Lim

**Ideal Rankine cycle example 3.14**

**• Ideal Rankine cycle**

**(100% efficiency turbine and pump)**

9

(1)

(2) (3)

(4)

(1)

(3) (2) (4)

𝜂_{𝑅𝑎𝑛𝑘𝑖𝑛𝑒} = 𝑤

𝑞_{𝐻} = 1108

3196 = 34.7%

### 600℃

### 10MPa

### 99.6℃

### 0.1MPa

### 99.6℃

### 0.1MPa

Saturated water v.f. 0.924 Superheated steam

Subcooled water

### 100.3℃

### 10MPa

SNU NAOE Y. Lim

**Ts diagram**

10

SNU NAOE Y. Lim

**Real Rankine cycle example 3.15**

**• Rankine cycle with 85% efficiency turbine and pump**

### 600℃

### 10MPa

### 99.6℃

### 0.1MPa

### 99.6℃

### 0.1MPa

Saturated water v.f. 0.999 Superheated steam

Subcooled water

### 100.8℃

### 10MPa

𝜂_{𝑅𝑎𝑛𝑘𝑖𝑛𝑒} = 𝑤

𝑞_{𝐻} = 938.5

3194 = 29.4%

(1)

(3) (2) (4)

𝜂_{𝑅𝑎𝑛𝑘𝑖𝑛𝑒} = 𝑤

𝑞_{𝐻} = 1108

3196 = 34.7%

SNU NAOE Y. Lim

**Carnot cycle and Rankine cycle**

**• Ex 3.14**

12

### T

### Entropy s

**3** **2**

**4** **1**

### 𝑞

_{𝐻}

### at P

_{H}

𝑞_{𝐶} at P_{C}

**1** **4**

**2**

**3**

𝑞_{𝐻}

𝑤_{𝑜𝑢𝑡}

𝑞_{𝐶}

**1** **2**

**4** **3**

𝑤_{𝑖𝑛}

**Carnot cycle**

**Carnot **
**cycle**

SNU NAOE Y. Lim

**Joule-Thomson effect(expansion)**

**• 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)**

𝑃_{1}, 𝑇_{1} 𝑃_{2}, 𝑇_{2}

(throttling process or Joule–Thomson process)

SNU NAOE Y. Lim

**JT process ≈ isenthalpic process**

### (Assume steady-state, KE&PE small, adiabatic)

**• Energy Balance (1** ^{st} **law, Open system)**

^{st}

### •

^{𝑑𝑈}

𝑑𝑡

### = ሶ 𝑄 + ሶ 𝑊

_{𝑠}

### + σ

_{𝑖𝑛}

### 𝑚 ሶ

_{𝑖}

### ℎ

_{𝑖}

### − σ

_{𝑜𝑢𝑡}

### 𝑚 ሶ

_{𝑜}

### ℎ

_{𝑜}

### • Since the gas spends so little time in the valve,

### there is no time for heat transfer. Since there is no component, the shaft work is near zero. If the

### kinetic energy difference is negligible, for st-st,

### • 0 = 0 + 0 + ሶ 𝑚

_{1}

### ℎ

_{1}

### − ሶ 𝑚

_{2}

### ℎ

_{2}

### • ℎ

_{1}

### = ℎ

_{2}

### (isenthalpic)

P_{1}, T_{1}, V_{1}, H_{1} P_{2}, T_{2}, V_{2}, H_{2}

ሶ

𝑚_{1} 𝑚ሶ_{2}

SNU NAOE Y. Lim

**Refrigeration cycle**

15

ሶ𝑄

### Air

(Cold:0~4℃)

(Hot:15~30 ℃)

SNU NAOE Y. Lim

**Refrigeration process**

**• Carnot cycle**

16

𝑄_{𝐻}

𝑄_{𝐶}

𝑊_{𝑖𝑛}

𝑊_{𝑜𝑢𝑡} 𝑊_{𝑠}

Boiler Condenser

Turbine

Pump

Compressor

Evaporator (heater)
𝑄_{𝐶}

𝑄_{𝐻}

Expander or valve Condenser

**Refrigeration cycle**

SNU NAOE Y. Lim

**Refrigeration cycle**

17

ሶ𝑄 ሶ𝑄

### Cold

(Cold)

### Hot Isenthalpic

### expansion

(Very Cold)

### Heat exchanger

(hot)

### Evaporator

(cold vapor)

High P Low P

Low P

Compressor

High P

(Very hot)

### Condenser

SNU NAOE Y. Lim

### 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

SNU NAOE Y. Lim

**Example**

**• R134a (Refrigerant 134a)**

19

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

### Condenser

### Evaporator

ሶ𝑄_{𝑒𝑣𝑎𝑝}
ሶ𝑄_{𝑐𝑜𝑛𝑑}

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

SNU NAOE Y. Lim

**Subcooling & Superheating**

**• Subcooling (Point 44’)**

**• Superheating (Point 22’)**

∴ 𝐶𝑂𝑃 =𝑄_{𝐶}ሶ

ሶ𝑊_{𝑐} = 𝑞_{𝐶}
𝑤_{𝐶}

1 2

3 4

1’ 2’

3’

4’ Saturated Liquid Subcooled Liquid

Saturated Vapor

Superheated Vapor

𝑞_{𝐶}

𝑤_{𝐶}

SNU NAOE Y. Lim

**Multi Compression**

**• Multi Compression**

### – ∆ℎ

_{2}

^{′}

_{1}

### > ∆ℎ

_{21}

### + ∆ℎ

_{43}

Condenser

Evaporator

Compressor Throttling (J-T)

Valve

T_{2}
T_{3}

𝑤_{𝐶} = ∆ℎ

∆ℎ_{21}

∆ℎ_{2}′1

∆ℎ_{43}

(T_{3}<T_{2})

SNU NAOE Y. Lim

**Simple liquefaction process**

22

SNU NAOE Y. Lim

**Linde-Hampson liquefaction process**

**• (1895)**

23

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

SNU NAOE Y. Lim

**Example 3.16**

**• n=? (0.73 mol/s in textbook)**

**• COP=? (3.22 in textbook)**

24

**PR**

0.72mol/s 3.21

SNU NAOE Y. Lim

**Exergy**

**• Energy is always conserved, but not all **

**that energy is available to do useful work.**

**• How can we define an useful energy that ** **we can use? Exergy**

25

### Hot T

_{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

SNU NAOE Y. Lim

**Exergy**

**• Exergy**

### – Available energy to be used.

### – The maximum useful work possible during a process that brings the system into equilibrium with its surroundings.

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

26

### Reversible Adiabatic Expansion

𝑃_{0}, 𝑇_{0}

𝑃_{1}, 𝑇_{1} 𝑃_{0}, 𝑇_{2}

𝑃_{0}, 𝑇_{0}

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

Carnot Cycle

𝑤𝑐𝑎𝑟𝑛𝑜𝑡 𝑐𝑦𝑐𝑙𝑒

𝑇_{0}

𝑃_{0}, 𝑇_{0}

Dead state

(no more useful work)

SNU NAOE Y. Lim

**Exergy**

**• Exergy b at state 1 can be defined as: **

**• If the macroscopic kinetic energy and ** **potential energy are not negligible:**

27

### 𝑏

_{1}

### ≡ 𝑢

_{1}

### − 𝑢

_{0}

### + 𝑃

_{0}

### 𝑣

_{1}

### − 𝑣

_{0}

### − 𝑇

_{0}

### 𝑠

_{1}

### − 𝑠

_{0}

Available internal energy

(comparing to the dead state)

Available PV work Entropy loss or heat loss

(or Available chemical energy)

### 𝑏

_{1}

### = 𝑢

_{1}

### − 𝑢

_{0}

### + 𝑃

_{0}

### 𝑣

_{1}

### − 𝑣

_{0}

### − 𝑇

_{0}

### 𝑠

_{1}

### − 𝑠

_{0}

### + 𝑉 ത

_{1}

^{2}

### 2 − 𝑉 ത

_{0}

^{2}

### 2 + 𝑔 𝑧

_{1}

### − 𝑧

_{0}

= 𝑢_{1} − 𝑢_{0} + 𝑃_{0} 𝑣_{1} − 𝑣_{0} − 𝑇_{0} 𝑠_{1} − 𝑠_{0} + 𝑉ത_{1}^{2}

2 + 𝑔𝑧_{1}

SNU NAOE Y. Lim

**Exergy in an open system**

### – This exergy in an open system is called as

### “exthalpy 𝑏 _{𝑓} ,” but many people use just exergy for both meaning.

28

### 𝑏

_{1}

### = 𝑢

_{1}

### − 𝑢

_{0}

### + 𝑃

_{0}

### 𝑣

_{1}

### − 𝑣

_{0}

### − 𝑇

_{0}

### 𝑠

_{1}

### − 𝑠

_{0}

### + 𝑃

_{1}

### − 𝑃

_{0}

### 𝑣

_{1}

### = 𝑢

_{1}

### + 𝑃

_{1}

### 𝑣

_{1}

### − 𝑢

_{0}

### + 𝑃

_{0}

### 𝑣

_{0}

### − 𝑇

_{0}

### 𝑠

_{1}

### − 𝑠

_{0}

### = ℎ

_{1}

### − ℎ

_{0}

### − 𝑇

_{0}

### 𝑠

_{1}

### − 𝑠

_{0}

SNU NAOE Y. Lim

**Example 3.18**

29

Q

ሶ

𝑚_{𝑎𝑖𝑟} = 30 kg/min
𝑇_{1} = 285 K

𝑃_{1} = 1 bar 𝑃_{2} = 1 bar

ሶ

𝑚_{𝑠𝑡𝑒𝑎𝑚} = 3 kg/min
𝑥_{3} = 0.9

𝑃_{3} = 10 bar
𝑥_{4} = 0.2

𝑃_{4} = 10 bar
**Ex 3.18 (exergy **
**loss)**

814.4 kJ/min (SRK)

SNU NAOE Y. Lim

**Example 3.18**

30 From h,s: -794 kJ/min

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

From ex: -813/-839

SNU NAOE Y. Lim

**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

SNU NAOE Y. Lim

**Exergy Analysis**

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