Week 2a Carnot Cycle

Lecture 2

Vapor Compression cycle Book:

Refrigeration & Air-Conditioning by Wilbert F. Stoecker / Jerold W. Jones(Chapter

Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle o The Carnot Cycle o Reversed Carnot Cycle o Carnot Heat pumps o Modifications in Ideal Carnot Cycle for practical reasons o Vapor Compression Cycle components o Introduction to PH charts o Performance of Standard VCC o Heat Exchangers o Actual Vapor Compression Cycle Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle The Carnot Cycle Ideal thermodynamically Reversible Cycle, first investigated by Sadi Carnot in 1824 A measure of the maximum possible conversion of heat energy into mechanical energy T2=T3

Heat from high temperature source

2

Work

3

Compressor

1

Turbine

4

Cool Liquid Heat rejected to low temperature sink

T1=T4

2

4

1

SA

Work

3

Entropy

SB

Process 1-2: Adiabatic Compression Process 2-3: isothermal addition of heat Process 3-4: adiabatic expansion Process 4-1: isothermal rejection of heat

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Vapor Compression cycle The Carnot Cycle Heat supplied during isothermal expansion (2-3)

T2=T3

2

3

= T2 (SB - SA) Heat rejected during isothermal compression (4-1) = T1 (SB

SA)

work done = Heat supplied = T2 (SB = (SB 



 

T1=T4

SA)

SA)(T2 

SA

Heat rejected

T1 (SB

SA)

T1) 

4

1

Entropy

SB

Process 1-2: adiabatic compression Process 2-3: isothermal addition of heat Process 3-4: adiabatic expansion Process 4-1: isothermal rejection of heat

Efficiency increases as T2 is increased and T1 is decreased Heat should be taken in, at as high temperature as possible and rejected at as low a temperature as possible. Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Reversed Carnot Cycle (i.e. Carnot Cycle for Refrigeration Cycle) A measure of the maximum performance to be obtained from a refrigerating machine Heat to high temperature source

3

2

3

2 Net Work

Compressor

Work

1

4

Turbine

Entropy

4

1

Cool Liquid Heat from low temperature sink

1-2: Adiabatic compression 2-3: Isothermal heat rejection 3-4: Adiabatic expansion 4-1: Isothermal addition of heat or isothermal expansion

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Vapor Compression cycle Reversed Carnot Cycle (i.e. Carnot Cycle for Refrigeration Cycle) Heat absorbed from the low temperature source in process 4-1 is the Refrigeration Step

3

2 Net Work

Carnot Cycle:

o o

1

4

A standard of comparison, A convenient guide to the temperatures that should be maintained to achieve maximum effectiveness

Entropy

1-2: Adiabatic compression 2-3: Isothermal heat rejection 3-4: Adiabatic expansion 4-1: Isothermal addition of heat or isothermal expansion

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Vapor Compression cycle Coefficient of Performance (COP) Ratio of out put to input would be misleading for a refrigeration system as the o/p in process 2-3 is usually wasted

3

2 Net Work 1

4





 

 

Entropy

1-2: Adiabatic compression 2-3: Isothermal heat rejection 3-4: Adiabatic expansion 

4-1: Isothermal addition of heat

 

or isothermal expansion

Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Conditions for Highest Coefficient of Performance Useful Refrigeration is the heat transferred in process 4-1, or the area beneath the line 4-1 Area underline 2-3 represents Rejected from the cycle

the

= T2 (S2 = (T2



S3)

T1) (S1

Heat Supplied

T1 (S1

2 Net Work

Heat

Area enclosed in rectangle 1-2-3-4 represents the Net Work Work done = Heat Rejected

3

1

4 Refrigeration

Entropy (S) KJ / Kg.K

S4)

S4) = Area of rectangle

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Vapor Compression cycle Coefficient of Performance (COP) COP indicates that a given amount of refrigeration requires only a small amount of work COP of the Reversed Carnot Cycle is entirely a function of the temperature limits and can vary from zero to infinity To obtain maximum possible COP

o Cold body temperature T1 should be as high as possible o Hot body temperature T2 should be as low as possible

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2 Net Work 1

4 Refrigeration

Entropy (S) KJ / Kg.K

1-2: Adiabatic compression 2-3: Isothermal heat rejection 3-4: Adiabatic expansion 4-1: Isothermal addition of heat or isothermal expansion 9

Vapor Compression cycle Temperature Limitations All refrigeration works against certain temperature limitations

o Cold room to be maintained at -20 oC or 253 K o Reject heat to the atmosphere at 30 oC or 303 K During Heat Rejection Process, refrigerant temperature must be higher than 303 K

30

oC

t

T

2

3 = 303 K

Atmosphere

-20 oC = 253 K

Cold Room

4

1 t

During the Refrigeration Process, refrigerant temperature must be lower than 253 K

Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Temperature Limitations we can keep the

as small as possible

t

T

Reduction of can be accomplished by increasing A or U in the heat exchange equation:

2

3

Atmosphere

Cold Room 1

4

t

Q=UA To decrease

to zero, either U or A would have to be infinite

S

Infinite values of U and A would also require an infinite cost

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Vapor Compression cycle Carnot Heat Pump

Heat Pump Refrigeration system operates for the purpose of delivering heat at a high level of temperature

Refrigeration cycle absorbs heat at a low temperature

Heat Pump rejects heat at a high temperature

Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Carnot Heat Pump Performance Factor

T 3





2





Net Work

 4

COP of Refrigeration Cycle with the same temperatures would be: T1/(T2 - T1).

 Performance Factor



 

1

Heat Rejected

S

 



Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Example 1 Carnot refrigeration cycle absorbs heat at 270 K and rejects heat at 300 K. (a) Calculate the coefficient of performance of this refrigeration cycle. (b) If the cycle is absorbing 1130 kJ/min at 270 K, how many kJ of work is required per second. (c) If the Carnot heat pump operates between the same temperatures as the above refrigeration cycle, what is its Performance Factor. (d) How many kJ/min will the heat pump deliver at 300 K if it absorbs 1130 kJ/min at 270 K.

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Vapor Compression cycle Example 2 The capacity of a refrigerator is 200 TR when working between

6 C and 25 oC.

Determine the mass of ice produced per day from water at 25 C. Also find the power required to drive the unit. Assume that the cycle operates on reversed Carnot cycle and latent heat of ice is 335 kJ/kg, Specific Heat of water is 4.187 KJ/Kg oC.

Mechanical Engineering Dept. CEME NUST

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Vapor Compression cycle Carnot Refrigeration Cycle for Vapor as Refrigerant If vapor/gas such as air is used as the refrigerant, cycle would differ from the familiar rectangle of the Carnot cycle. Cycle differs from the Carnot cycle by the addition of areas x and y

x 2 T

3

Atmosphere

Effect of area x is to increase the work required, which decreases the COP.

Cold Room

1 4

Effect of area y is to increase the work required and in addition reduce the amount of refrigeration

y S

Both these effects of areas x and y reduce the COP

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