Question 1

An Otto cycle with air as the working fluid has a compression ratio of 8.2. Under cold air standard conditions, the thermal efficiency of this cycle is
A)12%
B)43%
C)52%
D)57%
E)75%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
r=8.2
k=1.4
Eta_Otto=1-1/r^(k-1)
 
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 1/r "Taking efficiency to be 1/r"
W2_Eta = 1/r^(k-1) "Using incorrect relation"
W3_Eta = 1-1/r^(k1-1); k1=1.667 "Using wrong k value"

Question 2

For specified limits for the maximum and minimum temperatures, the ideal cycle with the lowest thermal efficiency is
A)Carnot
B)Stirling
C)Ericsson
D)Diesel
E)All are the same

Accepted Answer

The Diesel cycle typically has a lower thermal efficiency compared to the Carnot, Stirling, and Ericsson cycles when operating between the same temperature limits.

Question 3

A Carnot cycle operates between the temperatures limits of 400 K and 1600 K, and produces 3600 kW of net power. The rate of entropy change of the working fluid during the heat addition process is
A)0
B)1.8 kW/K
C)3.0 kW/K
D)2.3 kW/K
E)9.0 kW/K

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
TL=400 "K"
TH=1600 "K"
Wnet=3600 "kJ/s"
Wnet= (TH-TL)*DS
"Some Wrong Solutions with Common Mistakes:"
W1_DS = Wnet/TH "Using TH instead of TH-TL"
W2_DS = Wnet/TL "Using TL instead of TH-TL"
W3_DS = Wnet/(TH+TL) "Using TH+TL instead of TH-TL"

Question 4

Air in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under cold air standard conditions, the thermal efficiency of this cycle is
A)49.0%
B)38.6%
C)61.4%
D)67.0%
E)79.5%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
V1=4 "L"
V2= 0.25 "L"
V3= 0.50 "L"
r=V1/V2
rc=V3/V2
k=1.4
Eta_Diesel=1-(1/r^(k-1))*(rc^k-1)/k/(rc-1)
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 1-(1/r1^(k-1))*(rc^k-1)/k/(rc-1); r1=V1/V3 "Wrong r value"
W2_Eta = 1-Eta_Diesel "Using incorrect relation"
W3_Eta = 1-(1/r^(k1-1))*(rc^k1-1)/k1/(rc-1); k1=1.667 "Using wrong k value"
W4_Eta = 1-1/r^(k-1) "Using Otto cycle efficiency"

Question 5

Helium in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under air standard conditions, the thermal efficiency of this cycle is
A)20.5%
B)84.3%
C)79.5%
D)61.4%
E)67.4%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
V1=4 "L"
V2= 0.25 "L"
V3= 0.50 "L"
r=V1/V2
rc=V3/V2
k=1.667
Eta_Diesel=1-(1/r^(k-1))*(rc^k-1)/k/(rc-1)
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 1-(1/r1^(k-1))*(rc^k-1)/k/(rc-1); r1=V1/V3 "Wrong r value"
W2_Eta = 1-Eta_Diesel "Using incorrect relation"
W3_Eta = 1-(1/r^(k1-1))*(rc^k1-1)/k1/(rc-1); k1=1.4 "Using wrong k value"
W4_Eta = 1-1/r^(k-1) "Using Otto cycle efficiency"

Question 6

Helium gas in an ideal Otto cycle is compressed from 12<°C and 2 L to 0.25 L, and its temperature increases by an additional 800°C during the heat addition process. The temperature of helium before the expansion process is
A)1668°C
B)1182°C
C)1941°C
D)812°C
E)575°C

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.667
V1=2
V2=0.25
r=V1/V2
T1=12+273 "K"
T2=T1*r^(k-1)
T3=T2+800-273 "C"
"Some Wrong Solutions with Common Mistakes:"
W1_T3 =T22+800-273; T22=T1*r^(k1-1); k1=1.4 "Using wrong k value"
W2_T3 = T3+273 "Using K instead of C"
W3_T3 = T1+800-273 "Disregarding temp rise during compression"
W4_T3 = T222+800-273; T222=(T1-273)*r^(k-1) "Using C for T1 instead of K"

Question 7

In an ideal Otto cycle, air is compressed from 1.15 kg/m³ and 2.2 L to 0.26 L, and the net work output of the cycle is 620 kJ/kg. The mean effective pressure (MEP) for this cycle is A)713 kPa B)807 kPa C)638 kPa D)96 kPa E)367 kPa

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
rho1=1.15 "kg/m^3"
k=1.4
V1=2.2
V2=0.26
m=rho1*V1/1000 "kg"
w_net=620 "kJ/kg"
Wtotal=m*w_net
MEP=Wtotal/((V1-V2)/1000)
 
"Some Wrong Solutions with Common Mistakes:"
W1_MEP = w_net/((V1-V2)/1000) "Disregarding mass"
W2_MEP = Wtotal/(V1/1000) "Using V1 instead of V1-V2"
W3_MEP = (rho1*V2/1000)*w_net/((V1-V2)/1000); "Finding mass using V2 instead of V1"
W4_MEP = Wtotal/((V1+V2)/1000) "Adding V1 and V2 instead of subtracting"

Question 8

In an ideal Brayton cycle, air is compressed from 84 kPa and 25°C to 840 kPa. Under cold air standard conditions, the thermal efficiency of this cycle is
A)48%
B)52%
C)10%
D)60%
E)74%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
P1=84 "kPa"
P2=840 "kPa"
T1=25+273 "K"
rp=P2/P1
k=1.4
Eta_Brayton=1-1/rp^((k-1)/k)
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 1/rp "Taking efficiency to be 1/rp"
W2_Eta = 1/rp^((k-1)/k) "Using incorrect relation"
W3_Eta = 1-1/rp^((k1-1)/k1); k1=1.667 "Using wrong k value"

Question 9

Consider an ideal Brayton cycle executed between the pressure limits of 1100 kPa and 100 kPa and temperature limits of 20°C and 1200°C with argon as the working fluid. The net work output of the cycle is
A)136 kJ/kg
B)96 kJ/kg
C)227 kJ/kg
D)439 kJ/kg
E)456 kJ/kg

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
P1=100 "kPa"
P2=1100 "kPa"
T1=20+273 "K"
T3=1200+273 "K"
rp=P2/P1
k=1.667
Cp=0.5203 "kJ/kg.K"
Cv=0.3122 "kJ/kg.K"
T2=T1*rp^((k-1)/k)
q_in=Cp*(T3-T2)
Eta_Brayton=1-1/rp^((k-1)/k)
w_net=Eta_Brayton*q_in
"Some Wrong Solutions with Common Mistakes:"
W1_wnet = (1-1/rp^((k-1)/k))*qin1; qin1=Cv*(T3-T2) "Using Cv instead of Cp"
W2_wnet = (1-1/rp^((k-1)/k))*qin2; qin2=1.005*(T3-T2) "Using Cp of air instead of argon"
W3_wnet = (1-1/rp^((k1-1)/k1))*Cp*(T3-T22); T22=T1*rp^((k1-1)/k1); k1=1.4 "Using k of air instead of argon"
W4_wnet = (1-1/rp^((k-1)/k))*Cp*(T3-T222); T222=(T1-273)*rp^((k-1)/k) "Using C for T1 instead of K"

Question 10

An ideal Brayton cycle has a net work output of 220 kJ/kg and a backwork ratio of 0.4. If both the turbine and the compressor had an isentropic efficiency of 75%, the net work output of the cycle would be
A)165 kJ/kg
B)79 kJ/kg
C)293 kJ/kg
D)379 kJ/kg
E)182 kJ/kg

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
wcomp/wturb=0.4
wturb-wcomp=220 "kJ/kg"
Eff=0.75
w_net=Eff*wturb-wcomp/Eff
"Some Wrong Solutions with Common Mistakes:"
W1_wnet = Eff*wturb-wcomp*Eff "Making a mistake in Wnet relation"
W2_wnet = (wturb-wcomp)/Eff "Using a wrong relation"
W3_wnet = wturb/eff-wcomp*Eff "Using a wrong relation"

Question 11

In an ideal Brayton cycle, air is compressed from 100 kPa and 25°C to 800 kPa, and then heated to 1200°C before entering the turbine. Under cold air standard conditions, the air temperature at the turbine exit is
A)540°C
B)184°C
C)150°C
D)813°C
E)825°C

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
P1=100 "kPa"
P2=800 "kPa"
T1=25+273 "K"
T3=1200+273 "K"
rp=P2/P1
k=1.4
T4=T3*(1/rp)^((k-1)/k)-273
 
"Some Wrong Solutions with Common Mistakes:"
W1_T4 = T3/rp "Using wrong relation"
W2_T4 = (T3-273)/rp "Using wrong relation"
W3_T4 = T4+273 "Using K instead of C"
W4_T4 = T1+800-273 "Disregarding temp rise during compression"

Question 12

In an ideal Brayton cycle with regeneration, argon gas is compressed from 100 kPa and 25°C to 600 kPa, and then heated to 1200°C before entering the turbine. The highest temperature that argon can be heated in the regenerator is
A)337°C
B)246°C
C)586°C
D)719°C
E)446°C

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.667
Cp=0.5203 "kJ/kg.K"
P1=100 "kPa"
P2=600 "kPa"
T1=25+273 "K"
T3=1200+273 "K"
"The highest temperature that the gas can be heated in the regenerator is the turbine exit temperature,"
rp=P2/P1
T2=T1*rp^((k-1)/k)
T4=T3/rp^((k-1)/k)-273
 
"Some Wrong Solutions with Common Mistakes:"
W1_T4 = T3/rp "Using wrong relation"
W2_T4 = (T3-273)/rp^((k-1)/k) "Using C instead of K for T3"
W3_T4 = T4+273 "Using K instead of C"
W4_T4 = T2-273 "Taking compressor exit temp as the answer"

Question 13

In an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 10°C to 400 kPa and 180°C, is heated to 450°C in the regenerator, and then further heated to 1200°C before entering the turbine. Under cold air standard conditions, the effectiveness of the regenerator is
A)26%
B)42%
C)65%
D)57%
E)89%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.4
Cp=1.005 "kJ/kg.K"
P1=80 "kPa"
P2=400 "kPa"
T1=10+273 "K"
T2=180+273 "K"
T3=1200+273 "K"
T5=450+273 "K"
"The highest temperature that the gas can be heated in the regenerator is the turbine exit temperature,"
rp=P2/P1
T2check=T1*rp^((k-1)/k) "Checking the given value of T2. It checks."
T4=T3/rp^((k-1)/k)
Effective=(T5-T2)/(T4-T2)
"Some Wrong Solutions with Common Mistakes:"
W1_eff = (T5-T2)/(T3-T2) "Using wrong relation"
W2_eff = (T5-T2)/(T44-T2); T44=(T3-273)/rp^((k-1)/k) "Using C instead of K for T3"
W3_eff = (T5-T2)/(T444-T2); T444=T3/rp "Using wrong relation for T4"

Question 14

Consider a gas turbine that has a pressure ratio of 8 and operates on the Brayton cycle with regeneration between the temperature limits of 20°C and 900°C. If the specific heat ratio of the working fluid is 1.33, the highest thermal efficiency this gas turbine can have is
A)42%
B)49%
C)58%
D)63%
E)96%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.33
rp=8
T1=20+273 "K"
T3=900+273 "K"
Eta_regen=1-(T1/T3)*rp^((k-1)/k)
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 1-((T1-273)/(T3-273))*rp^((k-1)/k) "Using C for temperatures instead of K"
W2_Eta = (T1/T3)*rp^((k-1)/k) "Using incorrect relation"
W3_Eta = 1-(T1/T3)*rp^((k1-1)/k1); k1=1.4 "Using wrong k value (the one for air)"

Question 15

An ideal gas turbine cycle with many stages of compression and expansion and a regenerator of 100 percent effectiveness has an overall pressure ratio of 8. Air enters every stage of compressor at 290 K, and every stage of turbine at 1500 K. The thermal efficiency of this gas-turbine cycle is
A)19%
B)45%
C)65%
D)100%
E)81%

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.4
rp=8
T1=290 "K"
T3=1500 "K"
Eff=1-T1/T3
"Some Wrong Solutions with Common Mistakes:"
W1_Eta = 100
W2_Eta = 1-1/rp^((k-1)/k) "Using incorrect relation"
W3_Eta = 1-(T1/T3)*rp^((k-1)/k) "Using wrong relation"
W4_Eta = T1/T3 "Using wrong relation"

Question 16

Air enters a turbojet engine at 180 m/s at a rate of 20 kg/s, and exits at 850 m/s relative to the aircraft. The thrust developed by the engine is
A)17 kN
B)13 kN
C)0.8 kN
D)22 kN
E)34 kN

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
Vel1=180 "m/s"
Vel2=850 "m/s"
Thrust=m*(Vel2-Vel1)/1000 "kN"
m= 20 "kg/s"
"Some Wrong Solutions with Common Mistakes:"
W1_thrust = (Vel2-Vel1)/1000 "Disregarding mass flow rate"
W2_thrust = m*Vel2/1000 "Using incorrect relation"

Quiz 9: Gas Power Cycles

An Otto cycle with air as the working fluid has a compression ratio of 8.2. Under cold air standard conditions, the thermal efficiency of this cycle is

For specified limits for the maximum and minimum temperatures, the ideal cycle with the lowest thermal efficiency is

A Carnot cycle operates between the temperatures limits of 400 K and 1600 K, and produces 3600 kW of net power. The rate of entropy change of the working fluid during the heat addition process is

Air in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under cold air standard conditions, the thermal efficiency of this cycle is

Helium in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under air standard conditions, the thermal efficiency of this cycle is

Helium gas in an ideal Otto cycle is compressed from 12<°C and 2 L to 0.25 L, and its temperature increases by an additional 800°C during the heat addition process. The temperature of helium before the expansion process is

In an ideal Otto cycle, air is compressed from 1.15 kg/m3 and 2.2 L to 0.26 L, and the net work output of the cycle is 620 kJ/kg. The mean effective pressure (MEP) for this cycle is

In an ideal Brayton cycle, air is compressed from 84 kPa and 25°C to 840 kPa. Under cold air standard conditions, the thermal efficiency of this cycle is

Consider an ideal Brayton cycle executed between the pressure limits of 1100 kPa and 100 kPa and temperature limits of 20°C and 1200°C with argon as the working fluid. The net work output of the cycle is

An ideal Brayton cycle has a net work output of 220 kJ/kg and a backwork ratio of 0.4. If both the turbine and the compressor had an isentropic efficiency of 75%, the net work output of the cycle would be

In an ideal Brayton cycle, air is compressed from 100 kPa and 25°C to 800 kPa, and then heated to 1200°C before entering the turbine. Under cold air standard conditions, the air temperature at the turbine exit is

In an ideal Brayton cycle with regeneration, argon gas is compressed from 100 kPa and 25°C to 600 kPa, and then heated to 1200°C before entering the turbine. The highest temperature that argon can be heated in the regenerator is

In an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 10°C to 400 kPa and 180°C, is heated to 450°C in the regenerator, and then further heated to 1200°C before entering the turbine. Under cold air standard conditions, the effectiveness of the regenerator is

Consider a gas turbine that has a pressure ratio of 8 and operates on the Brayton cycle with regeneration between the temperature limits of 20°C and 900°C. If the specific heat ratio of the working fluid is 1.33, the highest thermal efficiency this gas turbine can have is

An ideal gas turbine cycle with many stages of compression and expansion and a regenerator of 100 percent effectiveness has an overall pressure ratio of 8. Air enters every stage of compressor at 290 K, and every stage of turbine at 1500 K. The thermal efficiency of this gas-turbine cycle is

Air enters a turbojet engine at 180 m/s at a rate of 20 kg/s, and exits at 850 m/s relative to the aircraft. The thrust developed by the engine is

In an ideal Otto cycle, air is compressed from 1.15 kg/m³ and 2.2 L to 0.26 L, and the net work output of the cycle is 620 kJ/kg. The mean effective pressure (MEP) for this cycle is