TITLE.PM5

658 ENGINEERING THERMODYNAMICS

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\M-therm\Th13-4.pm5

(i) 1-2—Heat rejection at constant pressure

(ii) 2-3—Adiabatic compression

(iii) 3-4—Addition of heat at constant volume

(iv) 4-1—Adiabatic expansion.

p

v

4

3

2 1

Adiabatic

Adiabatic

Fig. 13.30

Considering 1 kg of air.

Compression ratio =

v

v

2

3

= α

Expansion ratio = v

v

1

4

= r

Heat supplied at constant volume = cv(T 4 – T 3 )

Heat rejected = cv(T 1 – T 2 )

Work done = Heat supplied – heat rejected

= cv(T 4 – T 3 ) – cv(T 1 – T 2 )

η = Work done

Heat supplied

=

−− −

−

cT T cT T

cT T

v p

v

()()

()

43 12

43

= 1 – γ. ()

()

TT

TT

12

43

−

−

...(i)

During adiabatic compression 2-3,

T

T

v

v

3

2

2

3

1

=F^1

HG

I

KJ

=

−

−

γ

()αγ

or T 3 = T 2 ()αγ−^1 ...(ii)
During constant pressure operation 1-2,
v
T

v

T

1

1

2

2

=