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Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna Indian Institute of Technology Madras 4.1 Carnot Cycle : A Carnot gas cycle operating in a given temperature range is shown in the T-s diagram in Fig. 4.1(a). One way to carry out the processes of this cycle is through the use of steady-state, steady-flow devices as shown in Fig. 4.1(b). The isentropic expansion process 2-3 and the isentropic compression process 4-1 can be simulated quite well by a well-designed turbine and compressor respectively, but the isothermal expansion process 1-2 and the isothermal compression process 3-4 are most difficult to achieve. Because of these difficulties, a steady-flow Carnot gas cycle is not practical. The Carnot gas cycle could also be achieved in a cylinder-piston apparatus (a reciprocating engine) as shown in Fig. 4.2(b). The Carnot cycle on the p-v diagram is as shown in Fig. 4.2(a), in which processes 1-2 and 3-4 are isothermal while processes 2-3 and 4-1 are isentropic. We know that the Carnot cycle efficiency is given by the expression. 3 L 4 th H 1 2 T T T = 1 - = 1 - = 1 - T T T η

Module 4.1- Carnot Cycles

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Page 1: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

4.1 Carnot Cycle : A Carnot gas cycle operating in a given temperature range is shown in the T-s diagram

in Fig. 4.1(a). One way to carry out the processes of this cycle is through the use of

steady-state, steady-flow devices as shown in Fig. 4.1(b). The isentropic expansion

process 2-3 and the isentropic compression process 4-1 can be simulated quite well by

a well-designed turbine and compressor respectively, but the isothermal expansion

process 1-2 and the isothermal compression process 3-4 are most difficult to achieve.

Because of these difficulties, a steady-flow Carnot gas cycle is not practical.

The Carnot gas cycle could also be achieved in a cylinder-piston apparatus (a

reciprocating engine) as shown in Fig. 4.2(b). The Carnot cycle on the p-v diagram is as

shown in Fig. 4.2(a), in which processes 1-2 and 3-4 are isothermal while processes 2-3

and 4-1 are isentropic. We know that the Carnot cycle efficiency is given by the

expression.

3L 4th

H 1 2

TT T= 1 - = 1 - = 1 -

T T Tη

Page 2: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

1 2

4 3

TH

TL

T

(a)

heat inisothermal Turbine

Workout

Isentropic Turbine

Work out

Work in

heat out Isentropic compressor

IsothermalCompressor

Workin

1 2

3 4

Fig.4.1. Steady flow Carnot engine

Page 3: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

p 1

2

43

(a)

Pistondisplacement

Process 1 2: isothermalProcess 2 3: isentropic

Process 4 1: isentropicProcess 3 4: isothermal

(b)

Fig.4.2. Reciprocating Carnot engine

Page 4: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

Volume

1

2

3

4

Entropy

12

3 4T3=T4

T2=T1

Fig.4.3. Carnot cycle on p-v and T-s diagrams

Page 5: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

High temperatureSource

T K1

T K3

Low temperatureSink

Perfectly insulated walls

Perfect insulator cumPerfet conductor

Piston

Fig.4.4. Working of Carnot engine

Since the working fluid is an ideal gas with constant specific heats, we have, for the

isentropic process,

1131 4 2

4 1 3 3

VT V T ; =

T V T V

γ−γ−⎛ ⎞⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

Now, T1 = T2 and T4 = T3, therefore

34

1 2

vv = = r = compression or expansion ratio

v v

Carnot cycle efficiency may be written as,

th - 11 = 1 -

rγη

From the above equation, it can be observed that the Carnot cycle efficiency increases

as ‘r’ increases. This implies that the high thermal efficiency of a Carnot cycle is

Page 6: Module 4.1- Carnot Cycles

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna

Indian Institute of Technology Madras

obtained at the expense of large piston displacement. Also, for isentropic processes we

have,

11

1 1 2 2

4 4 3 3

T p T p = and =

T p T p

γ−γ−γγ ⎛ ⎞⎛ ⎞

⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

Since, T1 = T2 and T4 = T3, we have

1 2p

4 3

p p= = r = pressure ratio

p p

Therefore, Carnot cycle efficiency may be written as,

th 1

p

1 = 1 -

rγ −γ

η

From the above equation, it can be observed that, the Carnot cycle efficiency can be

increased by increasing the pressure ratio. This means that Carnot cycle should be

operated at high peak pressure to obtain large efficiency.