Study & Analysis of Carnot’s Model for Ideal Machine

P M V Subbarao

Professor

Mechanical Engineering Department

IIT Delhi

A True Concept of Blue Printing…….

A Mathematical Model for (James Watt’s) Steam Engine

expansion

Heat AdditionHeat Removal

Carnot Power Cycle

Goal: To generate Mechanical Power through from heat input !!!

Question: What is the Upper Limit of Engine Performance?

Can You Predict?

Is it essential to try and find out using only on the field Test?

Carnot’s Model for Power Cycle

compressorturbinenet WWW

s

– 2 : Compressor : Isentropic Compression : s2 = s1

2 – 3 : Boiler: Isothermal Heating : T3 = T2

3 – 4 : Turbines : Isentropic Expansion : s4 = s3

4 – 1 : Condenser: Isothermal Cooling : T1 = T4

Carnot’s Model for Power Cycle

Compressor : Isentropic Process

21 hhmW c

CVout

outin

inCV WgzVhmgzVhmQ

22

SSSF: Conservation of mass

inin mm

First Law :

No heat transfer, change in kinetic and potential energies are negligible

ssuming a single fluid entering and leaving…

Use the combined first and Second law statement for a reversible process.

2

1

12

2

1

vdpmhhmqm

Reversible Adiabatic Process:

2

1

21 vdpmhhmWcompressor

02

1

12

vdpmhhm

2 – 3 : Boiler: Isothermal Heating : T3 = T2

No work transfer, change in kinetic and potential energies are negligible

QCV

CVout

outin

inCV WgzVhmgzVhmQ

22

outoutininCV hmhmQ

ssuming a single fluid entering and leaving…

inoutCV hhmQ

3

2

23

3

2

vdpmhhmqm

For reversible constant Pressure & Temperature Process (change of phase)

23

3

2

hhmTdsm

2323max hhmssTm

Turbine : Isentropic Process :s4=s3

No heat transfer. Change in kinetic and potential energies are negligible

3

4

T

inin mmCMSSSF ::

CVout

outin

inCV WgzVhmgzVhmQ

22

CVoutoutinin Whmhm

ssuming a single fluid entering and leaving…

4

3

43 vdpmhhmhhmW outinCV

4 – 1 : Condenser : Isothermal Cooling : T3 = T2

No work transfer, change in kinetic and potential energies are negligible

QCV

CVout

outin

inCV WgzVhmgzVhmQ

22

outoutininCV hmhmQ

ssuming a single fluid entering and leaving…

41min ssTmhhmQ inoutCV

Analysis of Cycle

• First law for a cycle:

WQ

vdpmTdsm

41min23max ssTssTmW net

minmaxminmax

2143 &,

ssTTmW

ssssBut

net

additionHeat of Rate

outputPower Net cycle theof Efficiency

minmaxmax

minmaxminmax

ssTm

ssTTm

in

net

Q

W

max

min1T

T

minmaxminmaxoutput Work Specific ssTT

minmax

MEPvv

vdp

Work done per unit volume of the engine: Mean Effective Pressure

Carnot

inimize the capital & running costs.

Compact and efficient.

Use of Carnot Model for Optimization of Power Plant

A Major Crossroad Confusion: How to go from <6% to 75% Efficiency ???????

Rankine, William John Macquorn (1820-1872)

A MANUAL of the STEAM ENGINE and other PRIME MOVERS 1859 Rankine

• The conventional name work of the thermodynamics by Rankine.

• Rankine is the largest meritorious person who in addition raises the technology of the steam engine to science, the word, " energy " is something due to him.

• Harmony meaning of this work becomes " the manual of the steam engine and the other motive for action machines “.

• The chapter " of thermodynamics " advocated the cyclic process which is called Rankine cycle.

• This was related to the policy of researching the steam engine theoretically, brought the progress of the steam engine.

Rankine, William John Macquorn (1820-1872)• Rankine was born in Edinburgh and trained as a civil engineer.

From 1855 he was professor at Glasgow.• In 1849 he delivered two papers on the subject of heat, and in 1849 he

showed the further modifications required to French physicist Sadi Carnot's theory of thermodynamics.

• In A Manual of the Steam Engine and other Prime Movers 1859, Rankine described a thermodynamic cycle of events (the Rankine cycle).

• This came to be used as a standard for the performance of steam-power installations where a considerable vapour provides the working fluid.

• Rankine here explained how a liquid in the boiler vaporized by the addition of heat converts part of this energy into mechanical energy when the vapour expands in an engine.

• As the exhaust vapour is condensed by a cooling medium such as water, heat is lost from the cycle.

• The condensed liquid is pumped back into the boiler.