9-35
9-54 An ideal dual cycle has a compression ratio of 14 and cutoff ratio of 1.2. The thermal efficiency, amount of heat
added, and the maximum gas pressure and temperature are to be determined.
Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is
an ideal gas with constant specific heats.
Properties The properties of air at room temperature are cp = 1.005 kJ/kg·K, cv = 0.718 kJ/kg·K, R = 0.287 kJ/kg·K, and
k = 1.4 (Table A-2).
Analysis The specific volume of the air at the start of the compression is
v1 
RT1 (0.287 kPa  m 3 /kg  K )(253 K)

 0.9076 m 3 /kg
P1
80 kPa
and the specific volume at the end of the compression is
v2 
v1
r

x
2
3
qin
4
qout
0.9076 m 3 /kg
 0.06483 m 3 /kg
14
1
v
The pressure at the end of the compression is
v
P2  P1  1
v 2
P
k

  P1 r k  (80 kPa)141.4  3219 kPa

and the maximum pressure is
Px  P3  r p P2  (1.5)(3219 kPa)  4829 kPa
The temperature at the end of the compression is
and
k 1
v
T2  T1  1
v 2



P
T x  T2  3
 P2

 4829 kPa 
  (727.1 K)
  1091 K
 3219 kPa 

 T1 r k 1  (253 K)14 1.4 1  727.1 K
From the definition of cutoff ratio
v 3  rcv x  rcv 2  (1.2)(0.06483 m 3 /kg )  0.07780 m 3 /kg
The remaining state temperatures are then
v
T3  T x  3
v x

0.07780 
  (1091 K)
  1309 K

 0.06483 

v
T4  T3  3
v 4



k 1
 0.07780 
 (1309 K)

 0.9076 
1.4 1
 490.0 K
Applying the first law and work expression to the heat addition processes gives
q in  cv (T x  T2 )  c p (T3  T x )
 (0.718 kJ/kg  K )(1091  727.1)K  (1.005 kJ/kg  K )(1309  1091)K
 480.4 kJ/kg
The heat rejected is
q out  cv (T4  T1 )  (0.718 kJ/kg  K )(490.0  253)K  170.2 kJ/kg
Then,
 th  1 
q out
170.2 kJ/kg
 1
 0.646
480.4 kJ/kg
q in
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