GAS POWER CYCLES 641

dharm
\M-therm\Th13-3.pm5

Putting the value of T 2 in eqn. (ii), we get

T

T

r

3

1

β =()γ− 1

T 1 =

T

r

3

1

1

β γ

.

()−

Now inserting the values of T 1 , T 2 , T 4 and T 5 in eqn. (i), we get

η

ρ ρ

β

β

γρ

ρ

β

β

γρ

γ

γ γ γ

dual

..

()

()

()

()

=−

F

HG

I

KJ −

L

N

M

M

O

Q

P

P

F −

HG

I

KJ

+−

L

N

M

O

Q

P

=−

F −

HG

I

KJ

F −

HG

I

KJ

+−

−

− −

1

1

1

11

1 1 1

3

1

3

1

3 3 33

1

T

r

T

r

T T TT

r

i.e., η βρ
γ ββγρ

γ

dual ().

(. )

[( ) ( )]

=− −

− −+ −

1 11

r^111

...(13.10)

Work done is given by,

W = p 3 (v 4 – v 3 ) + pv^44 pv^55 pv^22 pv^11

11

−

−

− −

γγ−

= p 3 v 3 (ρ – 1) +

()pv prv43 53()pv prv23 13

1

ρ

γ

−−−

−

=

pv pv p

p

rpv p

p

33 43 5 r

4

23 1

2

11 1

1

()()ργ ρ

γ

−−+ −

F

HG

I

KJ

−−

F

HG

I

KJ

−

Also p

p

v

vr

5

4

4

5

=F

HG

I

KJ

=F

HG

I

KJ

γ ρ γ

and p

p

v

v

(^2) r
1
1
2
=F
HG
I
KJ

γ
γ
also, p 3 = p 4 , v 2 = v 3 , v 5 = v 1
∴ W = vp^33 p^3 r p r
1
2
11 11
1
[()()( )( )]
()
ργ ρρ
γ
−−+ −γγ− −γ
−
−−

pv 22 11 r^111 r
1
[( )( ) ( ) ( )]
()
βρ γ β ρ ρ
γ
−−+−γγ−−γ
−
−−

pr vr 11 11 r^11
1
() /[ (γγβγ ρ ) (β ) (βργ)]
γ
−+ −− −
−
−

pvr 11 1111 r 1
1
γγβγ ρ β βργ
γ
−−−+ −− −
−
[( )( ) ( )]
...(13.11)
Mean effective pressure (pm) is given by,
pm = W
vv
W
v r
r
pv r r
v r
r
(^121)
11
11
1
1
11 1
− 1 1

F −
HG
I
KJ
= −+ −− −
− FHG − IKJ
[()()()]−−
()
γγβγ ρ β βργ
γ
pm =
pr r
r
1
111 1
11
()[ ( ) ( ) ( )]
()()
γγβρ β βργ
γ
−+ −− −
−−
−
...(13.12)