Chapter 13: Gas Mixtures

Example 13-1 ,Page No.683

In [3]:
#given data
mO2=3.0;#moles of oxygen
mN2=5.0;#moles of nitrogen
mCH4=12.0;#moles of methane

#molecular masses in kg
MO2=32.0;
MN2=28.0;
MCH4=16.0;

#constants used
Ru=8.314;#in kJ/kg - K

#calculations

#part - a
mm=mO2+mN2+mCH4;
mfO2=mO2/mm;
mfN2=mN2/mm;
mfCH4=mCH4/mm;
print'mass fraction of oxygen is %f'%round(mfO2,2);
print'mass fraction of nitrogen is %f'%round(mfN2,2);
print'mass fraction of methane is %f'%round(mfCH4,2);

#part - b
NO2=mO2/MO2;
NN2=mN2/MN2;
NCH4=mCH4/MCH4;
Nm=NO2+NN2+NCH4;
yO2=NO2/Nm;
yN2=NN2/Nm;
yCH4=NCH4/Nm;
print'mole fraction of oxygen is %f'%round(yO2,3);
print'mole fraction of nitrogen is %f'%round(yN2,3);
print'mole fraction of methane is %f'%round(yCH4,3);

#part - c
Mm=mm/Nm;
print'average molecular mass %f kg/kmol'%round(Mm,1);
Rm=Ru/Mm;
print'gas constant of mixture %f kJ/kg - K'%round(Rm,3)
mass fraction of oxygen is 0.150000
mass fraction of nitrogen is 0.250000
mass fraction of methane is 0.600000
mole fraction of oxygen is 0.092000
mole fraction of nitrogen is 0.175000
mole fraction of methane is 0.734000
average molecular mass 19.600000 kg/kmol
gas constant of mixture 0.425000 kJ/kg - K

Example 13-2 ,Page No.687

In [1]:
#given data
NN2=2.0;#moles of nitrogen
NCO2=6.0;#moles of carbon dioxide
Tm=300.0;#temperature of gases in K
Pm=15000.0;#pressure of gases in kPa

#constants used
Ru=8.314;#in kJ/kmol - K

#calculations

#part - a
Nm=NN2+NCO2;
Vm=Nm*Ru*Tm/Pm;
print'the volume of the tank on the basis of the ideal-gas equation of state %f m^3'%round(Vm,3);

#part - b
#from Table A-1
#for nitrogen
TcrN=126.2;
PcrN=3390;
#for Carbondioxide
TcrC=304.2;
PcrC=7390;
yN2=NN2/Nm;
yCO2=NCO2/Nm;
Tcr=yN2*TcrN+yCO2*TcrC;
Pcr=yN2*PcrN+yCO2*PcrC;
Tr=Tm/Tcr;
Pr=Pm/Pcr;
#from Fig A-15b
Zm=0.49;
Vm=Zm*Nm*Ru*Tm/Pm;
print'the volume of the tank on the basis Kay’s rule %f m^3'%round(Vm,3);

#part - c
#for nitrogen
TrN=Tm/TcrN;
PrN=Pm/PcrN;
#from Fig A-15b
Zn=1.02;
#for Carbondioxide
TrC=Tm/TcrC;
PcrC=Pm/PcrC;
#from Fig A-15b
Zc=0.3;
Zm=yN2*Zn+yCO2*Zc;
Vm=Zm*Nm*Ru*Tm/Pm;
print'the volume of the tank on the basis compressibility factors and Amagat’s law %f m^3'%round(Vm,3);

#part - d
VRN=(Vm/NN2)/(Ru*TcrN/PcrN);
VRC=(Vm/NCO2)/(Ru*TcrC/PcrC);
#from Fig A-15b
Zn=0.99;
Zc=0.56;
Zm=yN2*Zn+yCO2*Zc;
Vm=Zm*Nm*Ru*Tm/Pm;
#When the calculations are repeated we obtain 0.738 m3 after the second iteration, 0.678 m3 after the third iteration, and 0.648 m3 after the fourth iteration.
Vm=0.648;
print'compressibility factors and Dalton’s law the volume of the tank on the basis %f m^3'%round(Vm,3);
the volume of the tank on the basis of the ideal-gas equation of state 1.330000 m^3
the volume of the tank on the basis Kay’s rule 0.652000 m^3
the volume of the tank on the basis compressibility factors and Amagat’s law 0.639000 m^3
compressibility factors and Dalton’s law the volume of the tank on the basis 0.648000 m^3

Example 13-3 ,Page No.691

In [3]:
#given data
mN=4.0;#mass of nitrogen in kg
T1N=20.0;#temperature of nitrogen in K
P1N=150.0;#pressure of nitrogen in kPa
mO=7.0;#mass of oxygen in kg
T1O=40.0;#temperature of oxygen in K
P1O=100.0;#pressure of oxygen in kPa

#molecular masses in kg
MO=32.0;
MN=28.0;

#constants used
Ru=8.314;#in kJ/kg - K

#from Table A-2a
CvN=0.743;
CvO=0.658;

#calculations

#part - a
#Ein - Eout = dEsystem
# (m*cv*dT)N2 + (m*cv*dT)= 0;
Tm= (mN*CvN*T1N+ mO*CvO*T1O)/(mN*CvN+mO*CvO);
print'the mixture temperature %f C'%round(Tm,1);

#part - b
NO=mO/MO;
NN=mN/MN;
Nm=NO+NN;
VO=NO*Ru*(T1O+273)/P1O;
VN=NN*Ru*(T1N+273)/P1N;#Exergy Destruction during Mixing of Ideal Gases
Vm=VO+VN;
Pm=Nm*Ru*(Tm+273)/Vm;  
print'the mixture pressure after equilibrium has been established %f kPa'%round(Pm,1)
the mixture temperature 32.200000 C
the mixture pressure after equilibrium has been established 114.500000 kPa

Example 13-4 ,Page No.692

In [7]:
from math import log

#given data
NO=3.0;#moles of oxygen 
NC=5.0;#moles of carbondioxide
T0=25+273.0;#temperature of gasses in K

#constants used
Ru=8.314;#in kJ/kg - K

#calculations
Nm=NO+NC;
yO=NO/Nm;
yC=NC/Nm;
#dSm= -Ru*(NO*log(yO)+NC*log(yC))
Sm=-Ru*(NO*log(yO)+NC*log(yC));
print'the entropy change %f kJ/K'%round(Sm);
Xdestroyed=T0*Sm/1000;
print'exergy destruction associated %f MJ'%round(Xdestroyed,1)
the entropy change 44.000000 kJ/K
exergy destruction associated 13.100000 MJ

Example 13-5 ,Page No.694

In [11]:
#given data
T1=220;#intial temperature in K
T2=160;#final temperature in K
Pm=10;#pressure of air in MPa
yN=0.79;#mole fraction of nitrogen
yO=0.21;#mole fractions of oxygen


#critical properties
#for Nitrogen
TcrN=126.2;
PcrN=3.39;
#for Oxygen
TcrO=154.8;
PcrO=5.08;

#constants used
Ru=8.314;#in kJ/kg - K

#from Tables A-18 & 19
#at T1
h1N=6391;
h1O=6404;
#for T2
h2N=4648;
h2O=4657;

#calculations
#part - a
qouti=yN*(h1N-h2N)+yO*(h1O-h2O);
print'the heat transfer during this process using the ideal-gas approximation %i kJ/kmol'%round(qouti);

#part - b
Tcrm=yN*TcrN+yO*TcrO;
Pcrm=yN*PcrN+yO*PcrO;
Tr1=T1/Tcrm;
Tr2=T2/Tcrm;
Pr=Pm/Pcrm;
#at these values we get
Zh1=1;
Zh2=2.6
qout=qouti-Ru*Tcrm*(Zh1-Zh2);
print'the heat transfer during this process using Kay’s rule %i kJ/kmol'%round(qout);

#part - c
#for nitrogen
TrN1=T1/TcrN;
TrN2=T2/TcrN;
PrN=Pm/PcrN;
#from Fig A-15b
Zh1n=0.9;
Zh2n=2.4;
#for Oxygen
TrO1=T1/TcrO;
TrO2=T2/TcrO;
PcrO=Pm/PcrO;
#from Fig A-15b
Zh1O=1.3;
Zh2O=4.0;
#from Eq 12-58
h12N=h1N-h2N-Ru*TcrN*(Zh1n-Zh2n);# h1 - h2 for nitrogen
h12O=h1O-h2O-Ru*TcrO*(Zh1O-Zh2O);# h1 - h2 for oxygen
qout=yN*h12N+yO*h12O;
print'the heat transfer during this process using Amagat’s law %i kJ/kmol'%round(qout);
the heat transfer during this process using the ideal-gas approximation 1744 kJ/kmol
the heat transfer during this process using Kay’s rule 3502 kJ/kmol
the heat transfer during this process using Amagat’s law 3717 kJ/kmol

Example 13-6 ,Page No.705

In [1]:
from math import log

#13.6 (d) answer not matching as float datatype is giving more accurate answer in comparison to textbook that has given approximate due to rounding off to two decimal places

#given data
mfs=0.0348;#salinity mass fraction
mfw=1-mfs;
T0=288.15;#temperature of sea water in K

#constants used
Mw=18;
Ms=58.44;
Rw=0.4615;
pm=1028;
Ru=8.314;

#calculations
#part - a
Mm=1/((mfs/Ms)+(mfw/Mw));
yw=mfw*Mm/Mw;
ys=1-yw;
print'the mole fraction of the water is %f'%round(yw,4);
print'the mole fraction of the saltwater is %f'%round(ys,5);

#part - b
wmin=-Ru*T0*(ys*log(ys)+yw*log(yw));
wm=wmin/Mm;
print'the minimum work input required to separate 1 kg of seawater completely into pure water and pure salts %f kJ'%round(wm,2);

#part - c
wmin=Rw*T0*log(1/yw);
print'the minimum work input required to obtain 1 kg of fresh water from the sea %f kJ'%round(wmin,2);

#part - d
Pmin=pm*Rw*T0*log(1/yw);
print'the minimum gauge pressure that the seawater must be raised if fresh water is to be obtained by reverse osmosis using semipermeable membranes %i kPa'%round(Pmin)
the mole fraction of the water is 0.989000
the mole fraction of the saltwater is 0.010980
the minimum work input required to separate 1 kg of seawater completely into pure water and pure salts 7.850000 kJ
the minimum work input required to obtain 1 kg of fresh water from the sea 1.470000 kJ
the minimum gauge pressure that the seawater must be raised if fresh water is to be obtained by reverse osmosis using semipermeable membranes 1510 kPa