# Variables
m = 6. #kg #mass of nitrogen
M = 28. #kg/kmol #molar mass of nitrogen
R = 8314.3 #kg/kmol
p = 1e5 #Pa #pressure
T = 27.+273 #K #temperature
# Calculations and Results
V = m*R*T/(p*M)
print "Volume occupied by nitrogen = %.3f m**3"%(V)
# Variables
p1 = 10. #bar #inital pressure
T1 = 273.+227 #K #inital temperature
v1 = 0.01 #m**3 #initial volume
p2 = 1. #bar #final pressure
T2 = 273.+27 #K #final temperature
# Calculations and Results
v2 = (p1/p2)*(T2/T1)*v1 #m**3 #final volume
print "Final volume = %.2f m**3"%(v2)
# Variables
p = 1. #bar #pressure
T = 50.+273 #°C #temperature
h = 324.6 #kJ/kg #enthalpy
R = 8.3143 #kJ/kmolK
M = 28.97 #kg/kmol
#Part (a)
print "Part a";
u = h - (R/M)*T #kJ/kg #internal energy
print "Internal energy = %.1f kJ/kg"%(u)
#Part (b)
print "Part b:i";
u = h - (R/M)*T #kJ/kg #internal energy
print "Enthalpy = %.1f kJ/kg"%(h)
print "Internal energy = %.1f kJ/kg"%(u)
print "Part b:ii";
u = h - (R/M)*T #kJ/kg #internal energy
print "Enthalpy = %.1f kJ/kg"%(h)
print "Internal energy = %.1f kJ/kg"%(u)
# Variables
Cv = 718 #J/kgK #specific at constant volume
M = 28.97 #kg/kmol #molar mass of air
R = 8314.3 #J/kmolK
# Calculations and Results
Cp = (R/M)+Cv #J/kgK #specific heat at constant pressure
print "Specific heat at constant pressure = %.0f J/kg K"%(Cp)
import math
from scipy.integrate import quad
# Variables
p1 = 1. #bar #initial pressure
T1 = 27.+273 #K #initial temperature
p2 = 10. #bar #final pressure
T2 = 327.+273 #K #final temperature
# Calculations and Results
#Part(a)
print "Part a";
def f2(T):
return 1.4-18.3*(T/100)**(-1.5)+38.3*(T/100)**(-2)-29.3*(T/100)**(-3)
delta_h = quad(f2,T1,T2)[0]
print "Increase in specific enthalpy = %.2f kJ/kg"%(delta_h)
#Part(b)
print "Part b";
def f3(T):
return 1.042
delta_h = quad(f3,T1,T2)[0]
print "Increase in specific enthalpy at Cp = 1.042 kJ/kgK) = %.2f kJ/kg"%(delta_h)
%matplotlib inline
from numpy import *
from matplotlib.pyplot import *
import math
# Variables
Cp = 1005. #J/kgK #specific heat at constant pressure
Cv = 718. #J/kgK #specific heat at constant volume
m = 1. #kg #mass of air
T1 = (27.+273) #K #initial temperature
p1 = 1e5 #Pa #initial pressure
p2 = p1/2. #Pa #final pressure
# Calculations and Results
#Part(a)
print "Parta";
R = Cp-Cv #J/kgK
V1_a = m*R*T1/p1 #m**3 #initial volume
V2_a = V1_a #m**3 #final volume
T2 = p2*V2_a/(m*R) #K #final temperature
print "Final temperature,T2 = %.1f K"%(T2)
#Part(b)
print "Partb";
V1_b = m*R*T1/p1 #m**3 #initial volume
V2_b = V1_b*(p1/p2) #m**3 #final volume
#Isothermal process => T1 = T2
print "Final temperature,T2 = %.1f K"%(T1)
#Part(c)
print "Partc";
R = Cp-Cv #J/kgK
y = Cp/Cv
V1_c = m*R*T1/p1 #m**3 #initial volume
V2_c = V1_c*(p1/p2)**(1/y) #m**3 #final volume
T2 = p2*V2_c/(m*R) #K #final temperature
print "Final temperature,T2 = %.0f K"%(T2)
#P-V diagram
P = [p1*1e-5, p2*1e-5]
V = [V1_a ,V1_a]
plot(V,P,'b') #plot for part(a)
V = linspace(V1_b,V2_b,100)
P = (p1*1e-5*V1_b)/V
plot(V,P,'g') #plot for part(b)
V = linspace(V1_c,V2_c,100)
P = (p1*1e-5*V1_c**y)/V**y
plot(V,P,'r') #plot for part(c)
xlabel('Volume in m**3')
ylabel('Pressure in bar')
suptitle('p-V diagram sought in example 9.6')
#legends(['Part (a)';'Part (b)';'Part (c)'],[2 3 5],opt=1)
import math
from numpy.linalg import solve
# Variables
p1 = 10e6 #N/m**2 #initial pressure
T1 = 273.+27 #K #inital temperature
V1 = 50.e-3 #m**3 #inital volume
M = 28. #g/mol #molecular mass
R = 8314.3/M #J/kgK
y = 1.4 #gamma
# Calculations and Results
#Part(a)
print 'Parta';
m = (p1*V1)/(R*T1)
print "Mass of nitrogen stored in bottle = %.3f kg"%(m)
#Part(b):(i)
print 'Partb:i';
p2 = 15e6 #N/m**2 #final pressure
V2 = V1 #m**3 #final volume
T2 = (p2*V2)/(m*R)
print "Temperature of nitrogen at maximum permitted temperature = %.1f K"%(T2)
#Part(b):(ii)
print 'Partb:ii';
C = solve([[1, -1.4],[1, -1]],[[0],[R]]) #J/kgK #C = [Cp;Cv]
delta_U = m*C[1]*(T2-T1)*.001 #kJ #Change in internal energy
print "Change in internal energy = %.1f kJ"%(delta_U)
#Part(b):(iii)
print 'Partb:iii';
delta_H = m*C[0]*(T2-T1)*.001 #kJ #Change in enthalpy
print "Change in enthalpy = %.1f kJ"%(delta_H)
#Part(b):(iv)
print 'Partb:iv';
delta_S = m*(C[1]*math.log(T2/T1)+R*math.log(V2/V1))*.001 #kJ/K #Change in entropy
print "Change in entropy = %.4f kJ/K"%(delta_S)
import math
# Variables
T1 = 800. #K #initial temperature
p1 = 1.5e6 #N/m**2 #initial pressure
T2 = 540. #K #final temperature
T2s = 485. #K #final temperature for reversible process
Q = 0. #adiabatic process
y = 1.4
Cv = 718. #J/kgK #specific heat at constant volume
# Calculations and Results
delta_U = Cv*(T2-T1) #kJ/kg #change in internal energy
W = (Q-delta_U)*.001 #kJ/kg #work done per kilogram
print "Work done per kilogram = %.1f kJ/kg"%(W);
p2 = p1*(T2s/T1)**(y/(y-1)) #N/m**2 #final pressure
delta_S = (y*Cv)*math.log(T2/T1)-(y*Cv-Cv)*math.log(p2/p1)
print "Change in entropy = %.3f kJ/kgK"%(delta_S*.001)
import math
# Variables
xCO2 = 0.1 #mole fraction of CO2
xO2 = .09 #mole fraction of O2
xCO = 0.01 #mole fraction of CO
xN2 = 0.8 #mole fraction of N2
# Calculations and Results
M = xCO2*44 + xO2*32 + xCO*28 + xN2*28 #kg/kmol #avg. molar mass
R = 8314.3/M #J/kgK #gas constant
yCO2 = xCO2*(44/M) #mass fraction of CO2
yO2 = xO2*(32/M) #mass fraction of O2
yCO = xCO*(28/M) #mass fraction of CO
yN2 = xN2*(28/M) #mass fraction of N2
print "Molar Mass = %.2f kg/kmol"%(M);
print "Gas constant = %.1f J/kgK"%(R);
print "Mass fraction of CO2 = %.4f "%(yCO2);
print "Mass fraction of O2 = %.4f "%(yO2);
print "Mass fraction of CO = %.4f "%(yCO);
print "Mass fraction of N2 = %.4f "%(yN2);
import math
# variables
m = 1.9 #kg
T = 273.+20 #K
p = 150.e3 #Pa
yO2 = 0.1 #mass fraction of O2
yN2 = 0.75 #mass fraction of N2
yCO2 = 0.12 #mass fraction of CO2
yCO = 0.03 #mass fraction of CO
# Calculations and Results
#Part(a)
print "Parta";
M = 1/((yO2/32)+(yN2/28)+(yCO/28)+(yCO2/44)) #kg/kmol #molar mass
print "Molar mass = %.2f kg/kmol "%(M)
R = 8314.3/M #J/kgK #Gas constant
print "Gas constant = %.2f J/kgK "%(R)
V = m*R*T/p #m**3 #Volume
#Part(b)
print "Partb"
xO2 = yO2*(M/32) #mole fraction O2
print "Mole fraction of O2 = %.3f"%(xO2)
pO2 = xO2*p #partial pressure O2
print "Partial pressure of O2 = %.2f kPa"%(pO2*.001)
VO2 = xO2*V #partial volume of O2
print "Partial volume of O2 = %.4f m**3"%(VO2)
xN2 = yN2*(M/28) #mole fraction N2
print "Mole fraction of N2 = %.3f"%(xN2)
pN2 = xN2*p #partial pressure N2
print "Partial pressure of N2 = %.2f kPa"%(pN2*.001)
VN2 = xN2*V #partial volume of N2
print "Partial volume of N2 = %.4f m**3"%(VN2)
xCO2 = yCO2*(M/44) #mole fraction CO2
print "Mole fraction of CO2 = %.3f"%(xCO2)
pCO2 = xCO2*p #partial pressure CO2
print "Partial pressure of CO2 = %.2f kPa"%(pCO2*.001)
VCO2 = xCO2*V #partial volume of CO2
print "Partial volume of CO2 = %.4f m**3"%(VCO2)
xCO = yCO*(M/28) #mole fraction CO
print "Mole fraction of CO = %.3f"%(xCO)
pCO = xCO*p #partial pressure CO
print "Partial pressure of CO = %.2f kPa"%(pCO*.001)
VCO = xCO*V #partial volume of CO
print "Partial volume of CO = %.4f m**3"%(VCO)
# note : rounding off error
import math
from numpy.linalg import solve
# Variables
R = 1841. #J/kgK #Gas constant
Cp = 6310. #J/kgK #specific heat at constant pressure
MN = 28. #kg/kmol #molar mass N2
MH = 2. #kg/kmol #molar mass H2
CpN = 1042. #J/kgK #specific heat of N2
CpH = 14210. #J/kgK #specific heat of H2
# Calculations and Results
Y = solve([[8314.3/MN, 8314.3/MH],[CpN, CpH]],[[R],[ Cp]])
YN = round(Y[0],1) #mass fraction of N2
YH = round(Y[1],1) #mass fraction of H2
XN = YN*(8314.3/(R*MN)) #volume fraction of N2
XH = YH*(8314.3/(R*MH)) #volume fraction of H2
print "Mass fraction of N2 = %.1f "%(YN)
print "Mass fraction of H2 = %.1f "%(YH)
print "Volume fraction of N2 = %.4f "%(XN)
print "Volume fraction of H2 = %.4f "%(XH)
# note : rounding off error
import math
# Variables
m = 1.9 #kg
T = 273.+20 #K
p = 150. #kPa
pdat = 100. #kPa #datum pressure
Tdat = 273. #K #datum temperature
yO2 = 0.1 #mass fraction of O2
yN2 = 0.75 #mass fraction of N2
yCO2 = 0.12 #mass fraction of CO2
yCO = 0.03 #mass fraction of CO
xO2 = 0.093 #mole fraction of O2
xN2 = 0.795 #mole fraction of N2
xCO2 = 0.081 #mole fraction of CO2
xCO = 0.031 #mole fraction of CO
R = 280.22 #J/kgK
M = 29.67 #kg/kmol #mixture molar mass
CpO2=0.922 #kJ/kgK
CpN2=1.042 #kJ/kgK
CpCO2=0.842 #kJ/kgK
CpCO=1.041 #kJ/kgK
#Part(a)
print "Parta";
Cp = yN2*CpN2 + yO2*CpO2 + yCO2*CpCO2 + yCO*CpCO #kJ/kgK # specific heat of mixture at constant pressure
Cv = Cp - R*.001 #specific heat of mixture at constant volume
print "Cp = %.3f kJ/kgK"%(Cp)
print "Cv = %.4f kJ/kgK"%(Cv)
#Part(b)
print "Partb";
U = m*(Cv*(T-Tdat)) #kJ #internal energy
print "Internal energy = %.2f kJ"%(U)
#Part(c)
print "Partc"
H = U + m*R*T*.001 #kJ #enthalpy
print "Enthalpy = %.1f kJ"%(H)
#Part(d)
print "Partd"
SO2 = CpO2*math.log(T/Tdat)-(8.3143/32)*math.log(xO2*(p/pdat)) #kJ/kgK #entropy of O2
SN2 = CpN2*math.log(T/Tdat)-(8.3143/28)*math.log(xN2*(p/pdat)) #kJ/kgK #entropy of N2
SCO2 = CpCO2*math.log(T/Tdat)-(8.3143/44)*math.log(xCO2*(p/pdat)) #kJ/kgK #entropy of CO2
SCO = CpCO*math.log(T/Tdat)-(8.3143/28)*math.log(xCO*(p/pdat)) #kJ/kgK #entropy of CO
S = m*(yO2*SO2+yN2*SN2+yCO2*SCO2+yCO*SCO) #kJ/K #entropy
print "Entropy = %.4f kJ/K"%(S)
import math
# Variables
V_He = 0.3 #m**3 #volume of Helium
p_He = 20e5 #Pa #pressure of Helium
T_He = 273.+30 #K #Temperature of Helium
V_O2 = 0.7 #m**3 #volume of O2
p_O2 = 6e5 #Pa #pressure of O2
T_O2 = 273.+2 #K Temperature of O2
R_He = 2077. #J/kgK
R_O2 = 260. #J/kgK
Cv_He = 3116. #J/kgK
Cv_O2 = 662. #J/kgK
# Calculations and Results
m_He = (p_He*V_He)/(R_He*T_He) #kg #mass of Helium
m_O2 = (p_O2*V_O2)/(R_O2*T_O2) #kg #mass of O2
T_ad = (m_He*Cv_He*T_He+m_O2*Cv_O2*T_O2)/(m_He*Cv_He+m_O2*Cv_O2) #K #Temperature after mixing
T_final = 300 #K #final temperature
Q = (Cv_He*m_He+Cv_O2*m_O2)*(T_final-T_ad) #J #Magnitude of heat transfer
print "Magnitude of heat transfer = %.2f kJ"%(Q*.001)
import math
# Variables
T_E = (273.+20) #K #temperature of ethane
p_E = 200. #kPa #pressure of ethane
T_M = 273.+45 #K #temperature of methane
p_M = 200. #kPa #pressure of methane
m_E = 9. #kg/s #mass rate of ethane
m_M = 4.5 #kg/s #mass rate of methane
Cp_E = 1766. #J/kgK #specific heat of ethane
Cp_M = 2254. #J/kgK #specific heat of methane
# Calculations and Results
#Part(a)
print "Parta";
T = (m_E*Cp_E*T_E+m_M*Cp_M*T_M)/(m_E*Cp_E+m_M*Cp_M) #K #mixture temperature
print "Mixture temperature = %.1f K"%(T)
#Part(b)
print "Partb";
R_E = 8314.3/30 #J/kgK #gas constant for ethane
R_M = 8314.3/16 #J/kgK #gas constant for methane
R = (m_E/(m_E+m_M))*R_E+(m_M/(m_E+m_M))*R_M #J/kgK #gas constant of mixture
M = 8314.3/R #kg/kmol #mixture molar mass
x_E = (m_E/(m_E+m_M))*(M/30) #mole fraction of ethane
x_M = (m_M/(m_E+m_M))*(M/16) #mole fraction of methane
delta_S_E = Cp_E*math.log(T/T_E) - R_E*math.log(x_E) #J/kgK #change in entropy of ethane
delta_S_M = Cp_M*math.log(T/T_M) - R_M*math.log(x_M) #J/kgK #change in entropy of methane
print "Rate of entropy production = %.4f kJ/sK"%((m_E*delta_S_E+m_M*delta_S_M)*.001)
# note : rounding off error