Chapter 1 Gas Power Cycle

1st law : closed system
Ideal gas:
and
Analysis of Ideal Diesel Cycle
Constant pressure heat transfer
2
P = const.
⇒ w = P ( v − v )
and
2
2
4 1
3
3
3
2
= − q = C ( T −T
)
Isentropic Process of Ideal gases
3
1
4
3
2
3
1
k
1v1
4
3
Pv = RT, dh = C dT
q = q = C (T −T
)
in
2
2
q = u − u = −C
( T −T
)
q
q = u − u + w
out
k
Pv = P
k
p
3
v
= P
2
2
4
2
k
2v2
P ⎛ 2 v ⎞ ⎛ 1 V ⎞ 1
= ⎜
⎟ = ⎜
⎟
P1
⎝ v2
⎠ ⎝V2
⎠
( k −1)
/ k
T ⎛ ⎞ ⎛ ⎞
2 P2
v1
= ⎜
⎟ = ⎜
⎟
T1
⎝ P1
⎠ ⎝ v2
⎠
3
q = u − u + P ( v − v ) = h − h
v
2
3
4
1
= constant
k
p
k −1
2
1
3
2
P
T
2
q in
v 2 =v 3
2
1
s 1 =s 2
3
Pv k = c
P = const.
Pv k = c
q in
v = const.
Analysis of Ideal Diesel Cycle
Cut off ratio (r c ) is the ratio of the cylinder
volume after and before the combustion process
Thermal
w
η th =
q
from
at
net
H
r c
efficiency
q
= 1 −
q
V3
v3
= =
V v
T1
( T4
/ T1
− 1)
= 1 −
kT ( T / T − 1)
2
definition
processes
3
out
in
of
2
2
1 − 2 and 3 − 4
2
T4
− T1
= 1 −
k ( T − T )
r
c
and
k
1 ⎡ r ⎤
c − 1
η th = 1 − k −1
⎢ ⎥
r ⎣ k ( rc
− 1)
⎦
3
2
isentropic
P
T
2
q in
v 2 =v 3
2
3
Pv k = c
1
s 1 =s 2
Pv k = c
P = const.
q in
v = const.
q out
4
1
v 1 =v 4
q out
4
1
v 1 =v 4
4
3
s3 =s 4
q out
v
4
3
s3 =s 4
q out
v
s
s