Question 1

An ideal gas mixture whose apparent molar mass is 48 kg/kmol consists of nitrogen N₂ and three other gases. If the mole fraction of nitrogen is 0.24, its mass fraction is A)0.24 B)0.14 C)0.41 D)0.86 E)0.70

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
M_mix=48 "kg/kmol"
M_N2=28 "kg/kmol"
y_N2=0.24
mf_N2=(M_N2/M_mix)*y_N2
"Some Wrong Solutions with Common Mistakes:"
W1_mf = y_N2 "Taking mass fraction to be equal to mole fraction"
W2_mf= y_N2*(M_mix/M_N2) "Using the molar mass ratio backwords"
W3_mf= 1-mf_N2 "Taking the complement of the mass fraction"

Question 2

An ideal gas mixture consists of 3 kmol of N₂ and 7 kmol of CO₂. The mass fraction of CO₂ in the mixture is A)0.214 B)0.700 C)0.500 D)0.652 E)0.786

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
N1=3 "kmol"
N2=7 "kmol"
N_mix=N1+N2
MM1=28 "kg/kmol"
MM2=44 "kg/kmol"
m_mix=N1*MM1+N2*MM2
mf2=N2*MM2/m_mix
 
"Some Wrong Solutions with Common Mistakes:"
W1_mf = N2/N_mix "Using mole fraction"
W2_mf = 1-mf2 "The wrong mass fraction"

Question 3

An ideal gas mixture consists of 4 kmol of N₂ and 6 kmol of CO₂. The apparent gas constant of the mixture is A)0.221 kJ/kg.K B)0.232 kJ/kg.K C)0.243 kJ/kg.K D)0.475 kJ/kg.K E)1.12 kJ/kg.K

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
Ru=8.314 "kJ/kmol.K"
N1=4 "kmol"
N2=6 "kmol"
MM1=28 "kg/kmol"
MM2=44 "kg/kmol"
R1=Ru/MM1
R2=Ru/MM2
N_mix=N1+N2
y1=N1/N_mix
y2=N2/N_mix
MM_mix=y1*MM1+y2*MM2
R_mix=Ru/MM_mix
"Some Wrong Solutions with Common Mistakes:"
W1_Rmix =(R1+R2)/2 "Taking the arithmetic average of gas constants"
W2_Rmix= y1*R1+y2*R2 "Using wrong relation for Rmixture"

Question 4

A rigid tank is divided into two compartments by a partition. One compartment contains 2 kmol of N₂ at 500 kPa pressure and the other compartment contains 8 kmol of CO₂ at 200 kPa. Now the partition is removed, and the two gases form a homogeneous mixture at 300 kPa. The partial pressure of N₂ in the mixture is A)41 kPa B)60 kPa C)150 kPa D)115 kPa E)225 kPa

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
P1 = 500 "kPa"
P2 = 200 "kPa"
P_mix=300 "kPa"
N1=2 "kmol"
N2=8 "kmol"
MM1=28 "kg/kmol"
MM2=44 "kg/kmol"
N_mix=N1+N2
y1=N1/N_mix
y2=N2/N_mix
P_N2=y1*P_mix
"Some Wrong Solutions with Common Mistakes:"
W1_P1= P_mix/2 "Assuming equal partial pressures"
W2_P1= mf1*P_mix; mf1=N1*MM1/(N1*MM1+N2*MM2) "Using mass fractions"
W3_P1 = P_mix*N1*P1/(N1*P1+N2*P2) "Using some kind of weighed averaging"

Question 5

A 100-L rigid tank contains an ideal gas mixture of 5 g of O₂ and 5 g of CO₂ at a specified pressure and temperature. If O₂ were separated from the mixture and stored at mixture temperature and pressure, its volume would be A)35 L B)39 L C)50 L D)58 L E)100 L

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
V_mix=100 "L"
m1=5 "g"
m2=5 "g"
MM1=32 "kg/kmol"
MM2=44 "kg/kmol"
N1=m1/MM1
N2=m2/MM2
N_mix=N1+N2
y1=N1/N_mix
V1=y1*V_mix "L"
"Some Wrong Solutions with Common Mistakes:"
W1_V1=V_mix*m1/(m1+m2) "Using mass fractions"
W2_V1= V_mix "Assuming the volume to be the mixture volume"

Question 6

An ideal gas mixture consists of 4 kg of Ar and 6 kg of CO₂ gases. The mixture is now heated at constant volume from 275 K to 325 K. The amount of heat transfer is A)485 kJ B)716 kJ C)519 kJ D)834 kJ E)1687 kJ

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
T1=225 "K"
T2=325 "K"
Cv1=0.3122; Cp1=0.5203 "kJ/kg.K"
Cv2=0.657; Cp2=0.846 "kJ/kg.K"
m1=4 "kg"
m2=6 "kg"
MM1=39.95 "kg/kmol"
MM2=44 "kg/kmol"
"Applying Energy balance gives Q=DeltaU=DeltaU_Ar+DeltaU_CO2"
Q=(m1*Cv1+m2*Cv2)*(T2-T1)
"Some Wrong Solutions with Common Mistakes:"
W1_Q = (m1+m2)*(Cv1+Cv2)/2*(T2-T1) "Using arithmetic average of properties" 
W2_Q = (m1*Cp1+m2*Cp2)*(T2-T1)"Using Cp instead of Cv"
W3_Q = (m1*Cv1+m2*Cv2)*T2 "Using T2 instead of T2-T1"

Question 7

An ideal gas mixture consists of 35% helium and 65% argon gases by mass. The mixture is now expanded isentropically in a turbine from 400°C and 1.2 MPa to a pressure of 150 kPa. The mixture temperature at turbine exit is
A)174°C
B)20°C
C)99°C
D)148°C
E)256°C

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
T1=400+273"K"
P1=1200 "kPa"
P2=150 "kPa"
mf_He=0.35
mf_Ar=0.65
k1=1.667
k2=1.667
"The specific heat ratio k of the mixture is also 1.667 since k=1.667 for all componet gases"
k_mix=1.667
T2=T1*(P2/P1)^((k_mix-1)/k_mix)-273
 
"Some Wrong Solutions with Common Mistakes:"
W1_T2 = (T1-273)*(P2/P1)^((k_mix-1)/k_mix) "Using C for T1 instead of K" 
W2_T2 = T1*(P2/P1)^((k_air-1)/k_air)-273; k_air=1.4 "Using k value for air"
W3_T2 = T1*P2/P1 "Assuming T to be proportional to P"

Question 8

One compartment of an insulated rigid tank contains 3 kmol of CO₂ at 20°C and 140 kPa while the other compartment contains 5 kmol of H₂ gas at 35°C and 280 kPa. Now the partition between the two gases is removed, and the two gases form a homogeneous ideal gas mixture. The temperature of the mixture is A)25°C B)28°C C)22°C D)32°C E)34°C

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
N_H2=5 "kmol"
T1_H2=35 "C"
P1_H2=280 "kPa"
N_CO2=3 "kmol"
T1_CO2=20 "C"
P1_CO2=140 "kPa"
Cv_H2=10.183; Cp_H2=14.307 "kJ/kg.K"
Cv_CO2=0.657; Cp_CO2=0.846 "kJ/kg.K"
MM_H2=2 "kg/kmol"
MM_CO2=44 "kg/kmol"
m_H2=N_H2*MM_H2
m_CO2=N_CO2*MM_CO2
"Applying Energy balance gives 0=DeltaU=DeltaU_H2+DeltaU_CO2"
0=m_H2*Cv_H2*(T2-T1_H2)+m_CO2*Cv_CO2*(T2-T1_CO2)
"Some Wrong Solutions with Common Mistakes:"
0=m_H2*Cp_H2*(W1_T2-T1_H2)+m_CO2*Cp_CO2*(W1_T2-T1_CO2) "Using Cp instead of Cv"
0=N_H2*Cv_H2*(W2_T2-T1_H2)+N_CO2*Cv_CO2*(W2_T2-T1_CO2) "Using N instead of mass"
W3_T2 = (T1_H2+T1_CO2)/2 "Assuming averate temperature"

Question 9

A piston-cylinder device contains an ideal gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 35°C and 420 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is
A)5.9 MJ
B)7.3 MJ
C)38 MJ
D)257 MJ
E)64 MJ

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
N_He=3 "kmol"
N_Ar=7 "kmol"
T1=35+273 "C"
P1=420 "kPa"
P2=P1
"T2=2T1 since PV/T=const for ideal gases and it is given that P=constant"
T2=2*T1 "K"
MM_He=4 "kg/kmol"
MM_Ar=39.95 "kg/kmol"
m_He=N_He*MM_He
m_Ar=N_Ar*MM_Ar
Cp_Ar=0.5203; Cv_Ar = 3122 "kJ/kg.C"
Cp_He=5.1926; Cv_He = 3.1156 "kJ/kg.K"
"For a P=const process, Q=DeltaH since DeltaU+Wb is DeltaH"
Q=m_Ar*Cp_Ar*(T2-T1)+m_He*Cp_He*(T2-T1)
 
"Some Wrong Solutions with Common Mistakes:"
W1_Q =m_Ar*Cv_Ar*(T2-T1)+m_He*Cv_He*(T2-T1) "Using Cv instead of Cp"
W2_Q=N_Ar*Cp_Ar*(T2-T1)+N_He*Cp_He*(T2-T1) "Using N instead of mass"
W3_Q=m_Ar*Cp_Ar*(T22-T1)+m_He*Cp_He*(T22-T1); T22=2*(T1-273)+273 "Using C for T1"
W4_Q=(m_Ar+m_He)*0.5*(Cp_Ar+Cp_He)*(T2-T1) "Using arithmetic averate of Cp"

Question 10

An ideal gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1500 K and 1 MPa at a rate of 0.25 kg/s, and expands isentropically to 200 kPa. The power output of the turbine is
A)366 kW
B)474 kW
C)570 kW
D)743 kW
E)1630 kW

Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
m=0.25 "kg/s"
T1=1200 "K"
P1=1500 "kPa"
P2=200 "kPa"
mf_He=0.5
mf_Ar=0.5
k_He=1.667
k_Ar=1.667
Cp_Ar=0.5203
Cp_He=5.1926
Cp_mix=mf_He*Cp_He+mf_Ar*Cp_Ar
"The specific heat ratio k of the mixture is also 1.667 since k=1.667 for all componet gases"
k_mix=1.667
T2=T1*(P2/P1)^((k_mix-1)/k_mix)
-W_out=m*Cp_mix*(T2-T1)
"Some Wrong Solutions with Common Mistakes:"
W1_Wout= - m*Cp_mix*(T22-T1); T22 = (T1-273)*(P2/P1)^((k_mix-1)/k_mix)+273 "Using C for T1 instead of K" 
W2_Wout= - m*Cp_mix*(T222-T1); T222 = T1*(P2/P1)^((k_air-1)/k_air)-273; k_air=1.4 "Using k value for air"
W3_Wout= - m*Cp_mix*(T2222-T1); T2222 = T1*P2/P1 "Assuming T to be proportional to P"
W4_Wout= - m*0.5*(Cp_Ar+Cp_He)*(T2-T1) "Using arithmetic average for Cp"

Quiz 13: Gas Mixtures

An ideal gas mixture whose apparent molar mass is 48 kg/kmol consists of nitrogen N2 and three other gases. If the mole fraction of nitrogen is 0.24, its mass fraction is

An ideal gas mixture consists of 3 kmol of N2 and 7 kmol of CO2. The mass fraction of CO2 in the mixture is

An ideal gas mixture consists of 4 kmol of N2 and 6 kmol of CO2. The apparent gas constant of the mixture is

A 100-L rigid tank contains an ideal gas mixture of 5 g of O2 and 5 g of CO2 at a specified pressure and temperature. If O2 were separated from the mixture and stored at mixture temperature and pressure, its volume would be

An ideal gas mixture consists of 4 kg of Ar and 6 kg of CO2 gases. The mixture is now heated at constant volume from 275 K to 325 K. The amount of heat transfer is

An ideal gas mixture consists of 35% helium and 65% argon gases by mass. The mixture is now expanded isentropically in a turbine from 400°C and 1.2 MPa to a pressure of 150 kPa. The mixture temperature at turbine exit is

A piston-cylinder device contains an ideal gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 35°C and 420 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is

An ideal gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1500 K and 1 MPa at a rate of 0.25 kg/s, and expands isentropically to 200 kPa. The power output of the turbine is

An ideal gas mixture whose apparent molar mass is 48 kg/kmol consists of nitrogen N₂ and three other gases. If the mole fraction of nitrogen is 0.24, its mass fraction is

An ideal gas mixture consists of 3 kmol of N₂ and 7 kmol of CO₂. The mass fraction of CO₂ in the mixture is

An ideal gas mixture consists of 4 kmol of N₂ and 6 kmol of CO₂. The apparent gas constant of the mixture is

A 100-L rigid tank contains an ideal gas mixture of 5 g of O₂ and 5 g of CO₂ at a specified pressure and temperature. If O₂ were separated from the mixture and stored at mixture temperature and pressure, its volume would be

An ideal gas mixture consists of 4 kg of Ar and 6 kg of CO₂ gases. The mixture is now heated at constant volume from 275 K to 325 K. The amount of heat transfer is