IE 211 INTRODUCTION TO ENGINEERING THERMODYNAMICS Chapter 6 Part2 ‘’The Second Law of Thermodynamics’’

CARNOT CYCLE

 Heat engines are cyclic devices that converts heat into work and cycle efficiency depends on reversibility of the processes  Reversible cycles provide upper limits on the performance of real engines  Best known reversible cycle is CARNOT CYCLE (cannot be achieved in reality)

CARNOT CYCLE composed of 4 reversible processes;

2 isothermal processes

+

2 adiabatic processes

occur either in a closed or steady-flow system

Frictionless piston-cylinder

4 reversible processes

REVERSIBLE ISOTHERMAL EXPANSION

 Constant T H  Reversible heat transfer during expansion ( system and reservoir temp. is nearly the same )

REVERSIBLE ADIABATIC EXPANSION

 Expansion with

insulation

(Q=0)  T H drops to T L  Reversible process(frictionless piston-cylinder)

WORK IS DONE BY THE SYSTEM REVERSIBLE ISOTHERMAL COMPRESSION

 Constant T L  Reversible heat transfer during compression ( system and sink temp. is nearly the same )

REVERSIBLE ADIABATIC COMPRESSION

 Compression with

insulation

(Q=0)  T L increases to T H  Reversible process(frictionless piston-cylinder)

WORK IS DONE BY THE SURROUNDINGS

CARNOT CYCLE

Area under 1-2-3

: work done by gas

Area under 3-4-1

: work done on the gas

REVERSED CARNOT CYCLE

Carnot cycle is reversible Processes may occur in the reverse direction

Refrigeration Carnot Cycle

THE CARNOT PRINCIPLES

 Related to thermal efficiency of reversible and irreversible (actual) heat engines

Q H W net,out Q L

 W net,out = Q H -Q L 

1)



th,2 (reversible) >



th,1 (irreversible ) 2)



th,2 (reversible) =



th,3 (reversible )

(for heat engines operating between the same reservoirs) (for heat engines operating between the same reservoirs)

Violation of either statement results in the violation of 2nd Law of Thermodynamics

THE THERMODYNAMIC TEMPERATURE SCALE

 Temp. Scale that is independent of properties of substances According 2 nd Carnot Principle

thermal efficiency of a reversible heat engine,



th ;



DEPENDS ON;

 Only on the temperature of reservoirs 

th, rev. = f(T H , T L )



INDEPENDENT OF;

   Working fluid and its properties The way the cycle is executed The type of reversible engine used



For reversible cycles, the heat transfer ratio can be replaced by the absolute temperature functions;

Kelvin proposed to define a temp. scale On Kelvin scale, temperature ratios depends on the ratios of heat transfer between a reversible heat engine and reservoirs only!

Absolute temp.s

 Water triple point was assigned the value 273.16 K

CARNOT HEAT ENGINE

 The theoretical heat engine that operates on the reversible Carnot cycle  Efficiency of any heat engine  Efficiency of

reversible

heat engine

CARNOT EFFICIENCY



Highest efficiency of a heat engine can have



An irreversible (actual) heat engines cannot reach this maximum value due to irreversibilities

COMPARISON of EFFICIENCIES OF REVERSIBLE AND IRREVERSIBLE HEAT ENGINES

 The thermal efficiency of actual heat engines can be maximized by supplying heat to at the highest possible temperature (T H ) (limited by material strength) and rejecting it at the lowest temperature possible(T L ) (limited by the temp. of river, lake, etc,..)

CARNOT REFRIGERATOR AND HEAT PUMP

 A refrigerator or heat pump operating on the reversed Carnot cycle  COP of any refrigerator  COP of any heat pump  COP of reversible refrigerator   COP of reversible heat pump  Highest coefficient of performance (COP) of refrigerator or heat pump operating between T H and T L can have

COMPARISON of EFFICIENCIES OF REVERSIBLE AND IRREVERSIBLE REFRIGERATORS

SUMMARY 2

nd

Law Thermal Efficiencies(



th

) and Coefficient of Performance (COP)

IRREVERSIBLE; REVERSIBLE; HEAT ENGINE REFRIGERATOR HEAT PUMP

STUDY QUESTIONS

1)

A coal-burning steam power plant produces a net power of 300 MW with an overall thermal efficiency of 32 percent. The actual gravimetric air –fuel ratio in the furnace is calculated to be 12 kg air/kg fuel. The heating value of the coal is 28,000 kJ/kg. Determine (

a

) the amount of coal consumed and heat rejected during a 24-hour (

b

) the rate of air flowing through the furnace. period

2)

An air conditioner removes heat steadily from a house at a rate of 750 kJ/min while drawing electric power at a rate of 6 kW.

Determine; (

a

) the COP of this air conditioner (it works as a refrigerator) (

b

) the rate of heat transfer to the outside air.

3)

A heat pump is used to maintain a house at a constant temperature of 23 ° C. The house is losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/h. For a COP of 2.5, determine the required power input to the heat pump.

4)

Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 35 ° C at a rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid. If the compressor consumes 1.2 kW of power, determine (

a

) the COP of the heat pump (

b

) the rate of heat absorption from the outside air.

5)

A Carnot heat engine receives 650 kJ of heat from a source of unknown temperature and rejects 250 kJ of it to a sink at 24 ° C. Determine, •Work output •Determine the thermal efficiency of the heat engine.

6)

An inventor claims to have developed a heat engine that receives 700 kJ of heat from a source at 500 K and produces 300 kJ of net work while rejecting the waste heat to a sink at 290 K. Is this a reasonable claim? Why?

7)

A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its temperature at -8 ° C. If the air surrounding the refrigerator is at 25 ° C, determine the minimum power input required for this refrigerator.

8)

The structure of a house is such that it loses heat at a rate of 5400 kJ/h per ° C difference between the indoors and outdoors. A heat pump that requires a power input of 6 kW is used to maintain this house at 21 ° C. Determine the lowest outdoor temperature for which the heat pump can meet the heating requirements of this house.

9)

A Carnot heat engine receives heat from a reservoir at 900 ° C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27 ° C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at -5 ambient air at 27 ° C. Determine ° C and transfers it to the same (

a

) the maximum rate of heat removal from the refrigerated space and (

b

) the total rate of heat rejection to the ambient air.