# Variables :
m = 500; #Kg
g = 7.925; #m/s**2
Z = 40; #Km
C = 2400; #Kmph
# Calculations and Results
PE = m*g*Z*1000; #Nm
print ("Relative to earth.");
print "Potential Energy in Nm : %.3e"%PE
KE = m*(C*1000./3600)**2/2; #Nm
print "Kinetic Energy in Nm : %.3e"%KE
print ("Relative to moon.");
w = 2.94*m; #Nm
PE = w*Z*1000; #Nm
print "Potential Energy in Nm : %.2e"%PE
KE = m*(C*1000./3600)**2/2; #Nm
print "Kinetic Energy in Nm : %.3e"%KE
# Variables :
VGR = 57.; #KN/m**2
Patm = 765.; #mm of Hg
# Calculations
#101.325KN/m**2 = 760 mm of Hg
VGR = VGR*760/101.325; #mm og Hg
Pabs = Patm-VGR; #mm of Hg
# Results
print "Absolute pressure in mm of Hg : %.2f"%(Pabs)
# Variables :
g = 9.81; #m/s**2
rho_o = 0.825*10**3; #Kg/m**3
rho_w = 1.*10**3; #Kg/m**3
rho_Hg = 13.45*10**3; #Kg/m**3
h_o = 50./100; #m
h_w = 65./100; #m
h_Hg = 45./100; #m
Patm = 1.01325; #bar
# Calculations and Results
P_Hg = rho_Hg*g*h_Hg; #N/m**2
P_w = rho_w*g*h_w; #N/m**2
P_o = rho_o*g*h_o; #N/m**2
Pbase = (Patm*10**5+P_Hg+P_o+P_w); #N/m**2
print "Pressure at the base of column in N/m**2 : %.5e"%Pbase
P_OilWater = Patm*10**5+P_o; #N/m**2
print "Pressure at the oil-water surface in N/m**2 : %.5e"%P_OilWater
P_WaterMercury = Patm*10**5+P_o+P_w; #N/m**2
print "Pressure at the water-mercury surface in N/m**2 : %.5e"%P_WaterMercury
#Answer in the book is not accurate.
import math
# Variables :
rho = 1000.; #Kg/m**3
d = 0.3; #m
C = 1.5; #m/s
h = 4.5; #m
FlowRate = 2000. #Kg/min
d2 = 15./100; #diameter of discharging line in meter
t = 15. #min
r = 3. #m
# Calculations and Results
WaterDischarge = rho*math.pi/4*(d/2)**2*C*t*60; #Kg
WaterReceived = FlowRate*t; #Kg
NetWaterReceived = WaterReceived-WaterDischarge; #Kg
print "Mass change in tank in Kg : %.1f"%(NetWaterReceived)
#m = rho*A*h
h = NetWaterReceived/rho/(math.pi/4*r**2); #m
print "Water level in meter : %.4f"%(h)
# Variables :
Pmercury = 10.; #cm of Hg
Patm = 76. #cm of Hg
# Calculations
Pwater = 3.5/13.6 #cm of Hg
Pabs = Pmercury+Patm-Pwater; #cm of Hg
Pabs = Pabs/76*1.01325; #bar
# Results
print "Absolute pressure of steam in bar : %.4f"%(Pabs)
# Variables :
Pmercury = 10.; #cm of Hg
Patm = 760. #mm of Hg
Patm = 1.01325 #bar
Pabs = 1.2 #bar
sg_oil = 0.8;
sg_water = 13.6;
sg_mercury = 13.6;
rho_w = 1000. #Kg.m**3
g = 9.81; #gravity constant
# Calculations and Results
deltaP = Pabs-Patm; #bar
deltaP = deltaP*10**5; #N/m**2
#deltaP = rho_o*g*h_o
rho_o = sg_oil*rho_w; #kg/m**3
h_o = deltaP/rho_o/g; #m
print "Height of fluid in oil manometer in meter : %.4f"%(h_o)
h_w = deltaP/rho_w/g; #m
print "Height of fluid in water manometer in meter : %.4f"%(h_w)
rho_m = sg_mercury*rho_w; #kg/m**3
h_m = deltaP/rho_m/g; #m
print "Height of fluid in mercury manometer in meter : %.4f"%(h_m)
# Variables :
Patm = 75. #mm of Hg
Patm = Patm*1.01325/76; #bar
rho = 800. #Kg.m**3
h = 30/100. #m
g = 9.81 #gravity constant
# Calculations
deltaP = rho*g*h*10**-5; #bar
Pabs = deltaP+Patm; #bar
# Results
print "Absolute pressure of gas in bar : %.6f"%(Pabs)
# Variables :
h1 = 5.1/100; #m
h2 = 10./100; #m
Patm = 75.5; #mm of Hg
Patm = Patm*1.01325/76*10**5; #bar
sg_k = 0.8;
sg_Hg = 13.6;
rho_w = 1000. #Kg/m**3
g = 9.81; #gravity constant
# Calculations
P_kerosine = sg_k*rho_w*g*h1; #N/m**2
P_Hg = sg_Hg*rho_w*g*h2 #N/m**2
Pabs = P_Hg+Patm-P_kerosine; #Nm**2
# Results
print "Absolute pressure of gas in KPa : %.2f"%(Pabs/1000)
from numpy import *
import math
# Variables :
t_ice = 0; #degree centigrade
p_ice = 1.5;
t_steam = 100; #degree centigrade
p_steam = 7.5;
# Calculations
#t = a*math.log(p)+b
#solving for a and b by matrix
A = array([[math.log(p_ice), 1],[math.log(p_steam) ,1]])
B = array([t_ice,t_steam])
#X = A**-1*B;
X = linalg.solve(A,B)
a = X[0]
b = X[1]
p = 3.5; #bar
t = a*math.log(p)+b; #degree C
# Results
print "Temperature scale in degree C : %.2f"%t
# Variables :
theta1_p1 = 273.16; #K
p_gauge1 = 32.; #mm of Hg
p_atm = 752.; #mm of Hg
p_gauge2 = 76.; #mm of Hg
# Calculations
P1 = p_gauge1+p_atm; #mm of Hg
P2 = p_gauge2+p_atm; #mm of Hg
theta2_p2 = theta1_p1*(P2/P1); #in K
theta2_p2 = theta2_p2-273; #degree C
# Results
print "Temperature in degree C : %.2f"%theta2_p2
# Variables :
R0 = 2.8; #ohm
t0 = 0; #degree C
R1 = 3.8; #ohm
t1 = 100; #degree C
R2 = 5.8; #ohm\
# Calculations
#R = R0*(1+alfa*t)
alfa = (R1/R0-1)/t1;
t2 = (R2/R0-1)/alfa; #degree C
# Results
print "Temperature at R2 in degree C : ",t2
# Variables :
#F = 2*C;
FbyC = 2;
# Calculations
C = 32./(FbyC-9./5); #degree C
F = C*FbyC; #degree F
# Results
print "Temperature fluid in degree R : ",F+460
print "Temperature fluid in degree K : ",C+273
import math
from numpy import *
# Variables :
T1 = 0.; #degree centigrade
K1 = 1.83;
T2 = 100.; #degree centigrade
K2 = 6.78;
# Calculations
#T = a*math.log(K)+b
#solving for a and b by matrix
A = array([[math.log(K1),1],[math.log(K2), 1]])
B = array([T1,T2])
X = linalg.solve(A,B)
a = X[0]
b = X[1]
K = 2.42; #bar
T = a*math.log(K)+b; #degree C
# Results
print "Temperature in degree C : %.3f"%T
# Variables :
#t = N/30-100/3
#t = N
# Calculations
N = (-100./3)/(1-1./30); #degree C
# Results
print "Temperatur at which degree C equals to degree N(degree C) : %.2f"%N
# Variables :
#epsilon = 0.2*t-5*10**-4*t**2; #mV
t_ice = 0. #degree C
epsilon_ice = 0.2*t_ice-5*10**-4*t_ice**2; #mV
t_steam = 100. #degree C
epsilon_steam = 0.2*t_steam-5*10**-4*t_steam**2; #mV
#At t = 60;
t = 60; #degree C
# Calculations
epsilon = 0.2*t-5*10**-4*t**2; #mV
reading = (t_steam-t_ice)/(epsilon_steam-epsilon_ice)*(epsilon-epsilon_ice)
# Results
print "Thermometer will read(degree C) : ",reading
import math
from numpy import *
# Variables :
tA1 = 0.; #degree centigrade
tB1 = 0.; #degree centigrade
tA2 = 100. #degree centigrade
tB2 = 100. #degree centigrade
#tA = l+m*tB+n*tb**2
l = 0; #by putting tA and tB equals to zero
#tA = m*tB+n*tB**2
#Thermometer immersed in oil bath
tA1 = 51.; #degree centigrade
tB1 = 50.; #degree centigrade
#solving for m and n by matrix
A = array([[tB1 ,tB1**2],[tB2, tB2**2]])
B = array([tA1,tA2])
# Calculations and Results
X = linalg.solve(A,B);
m = X[0]
n = X[1]
tA = 25; #degree centigrade
P = [n ,m ,-tA]; #polynomial for calculation of tB
tB = roots(P);
tB = tB[1]; #neglecting +ve sign
print "When A reads 25 degree C, B reading in degree C : %.3f"%tB
#let tB = 25; #degree C
tB = 25; #degree C
tA = l+m*tB+n*tB**2; #degree C
print "When B reads 25 degree C, A reading in degree C : ",tA
print ("B is correct. A shows error greater than B.")
#Answer is not accurate in the book.
# Variables :
p = 10.; #bar
T = 327.+273; #K
M = 42.4;
m = 1. #Kg
Rdegree = 8314.3; #Nm/KgK
# Calculations and Results
R = Rdegree/M; #Nm/KgK
V = m*R*T/p/10**5; #m**3/Kg
print "Specific volume in m**3/Kg ; %.4f"%V
rho = m/V; #Kg/m**3
print "Density of gas in Kg/m**3 : %.3f"%rho
# Variables :
Rdegree = 8314.3; #Universal Gas Consmath.tant
M = 32. #Molecular weight of gas
p1 = 3*10.**6. #N/m**2
V1 = 250*10.**-3 #m**3
T1 = 20+273. #K
p2 = 1.8*10**6 #N/m**2
V2 = V1; #m**3
T2 = 16+273. #K
# Calculations
R = Rdegree/M; #Nm/KgK
m1 = p1*V1/R/T1; #Kg
m2 = p2*V2/R/T2; #Kg
mass_used = m1-m2; #Kg
# Results
print "Mass of oxygen used in Kg : %.4f"%mass_used
import math
# Variables :
Rdegree = 8314.3; #Universal Gas Consmath.tant
r = 12. #meter
Patm = 75. #cm of Hg
Patm = Patm/76*1.01325*10**5; #N/m**2
V = 4./3*math.pi*r**3; #m**3
M_air = 28.97;
M_H2 = 2.
Tair = 18.+273; #K
g = 9.81; #gravity consmath.tant
# Calculations and Results
Rair = Rdegree/M_air; #Nm/KgK
RH2 = Rdegree/M_H2; #Nm/KgK
#p*V = m*R*T
m_air = Patm*V/Rair/Tair; #Kg
print "Mass of air in kg : %.2f"%m_air
n_air = m_air/M_air; #moles
print "No. of moles : %.2f"%n_air
m_H2 = n_air*M_H2; #Kg
print "Mass of H2 in kg : %.2f"%m_H2
Load = g*(m_air-m_H2); #N
print "Load balloon can lift in N ; %.1f"%Load
# Variables :
p1 = 1. #bar
p2 = 0.45; #bar
R = 287. #KJ/KgK
V = 40. #m**3
V1 = 40. #m**3
V2 = 40. #m**3
T1 = 35.+273; #K
T2 = 5.+273; #K
# Calculations
m = p1*10**5*V1/R/T1-p2*10**5*V2/R/T2
# Results
print "Mass of air removed in Kg : %.2f"%m
# Variables :
m = 1. #Kg
t = 80. #degree C
mw = 10. #Kg
t1 = 25. #degree C
delta_t = 5; #degree C
# Calculations
t2 = delta_t+t1; #degree C
Sw = 4.187; #Kj/KgK
#m*S*(t-t2) = mw*Sw*(t2-t1)
S = mw*Sw*(t2-t1)/m/(t-t2); #Kj/KgK
# Results
print "Specific heat of metal in KJ/KgK : ",S
# Variables :
m = 500.; #Kg
t1 = 45.; #degree C
t0 = 5.; #degree C
CP = 4.18; #KJ/Kg-degree C
Qdot = 41.87; #MJ/hr
# Calculations
Q = m*CP*(t1-t0); #KJ
Q = Q/1000; #MJ
Time = Q/Qdot; #hrs
# Results
print "Time required in hours : %.5f"%Time
import scipy
from scipy.integrate import quad
# Variables :
V1 = 2; #m**3
V2 = 4; #m**3
# Calculations
def f24(V):
return 10**5*(V**2+6*V)
W = quad(f24,V1,V2)[0]
W = W/1000.; #KJ
# Results
print "Work done in KJ : %.1f"%W
import math
from scipy.integrate import quad
# Variables :
p1 = 3.; #bar
V1 = 0.18; #m**3/Kg
p2 = 0.6; #bar
C = p1*10**5*V1**2; #Nm
V2 = math.sqrt((p1/p2)*V1**2); #m**3Kg
# Calculations
def f27(V):
return C/V**2
W = quad(f27,V1,V2)[0]
W = W/1000; #KJ/Kg
# Results
print "Work done in KJ/Kg : %.3f"%W
import math
from numpy import *
# Variables :
W = 160. #kJ
W = W*1000. #J
V1 = 800. #litres
V1 = V1/1000. #m**3
# Calculations
#p = 7-3*V
#[7*(V2-V1)-1.5*(V2**2-V1**2)]-W/10**5 = 0; #Nm or J
#7*V2-7*V1-1.5*V2**2+1.5*V1**2-W/10**5; #Nm or J
#P = [-10**5*1.5 10**5*7 -10**5*7*V1+10**5*1.5*V1**2-W]
P = array([-1.5, 7, -7*V1+1.5*V1**2-W/10**5])
V2 = roots(P); #m**3
V2 = V2[1] #(V2(1) gives -ve value which is not possible)
print "Final Volume in m**3 : %.4f"%V2
P2 = 7-3*V2; #bar
print "Final Pressure in bar : %.3f"%P2
#Answer is wrong in the book as calculation is wrong for V2.
import scipy
from scipy.integrate import quad
# Variables :
p0 = 1. #bar
p0 = p0*10**5; #N/m**2
V1 = 0; #m**3
V2 = 0.7; #m**3
# Calculations
#No p.dV work for cylinder as boundaries are
def f18(V):
return 1.
W = p0* quad(f18,V1,V2)[0]
W = W/1000.; #KJ/Kg
# Results
print "Workdone by the system in KJ : ",W
import scipy
from scipy.integrate import quad
# Variables :
p0 = 101.3; #KPa
V1 = 1.2; #m**3
V2 = 0; #m**3
# Calculations
def f6(V):
return 1
W = p0* quad(f6,V1,V2)[0]
# Results
print "Workdone by the air in KJ : ",W
import scipy
from scipy.integrate import quad
# Variables :
T1 = 300; #K
T2 = 2300; #K
Gamma = 1.5;
m = 1; #Kg
# Calculations and Results
def f14(T):
return m*(0.85+0.00004*T+5*10**-5*T**2)
H2subH1 = quad(f14,T1,T2)[0]
print "Change in enthalpy in KJ/Kg : %.1f"%H2subH1
def f15(T):
return m*(0.85+0.00004*T+5*10**-5*T**2)/Gamma
U2subU1 = quad(f15,T1,T2)[0]
print "Change in internal energy in KJ : %.1f"%U2subU1
# Variables :
m = 1.; #Kg
v = 1.; #m**3
T = 127.+273; #K
a = 138.; #KNm**4/(Kgmol)**2
a = a*10.**3; #Nm**4/(Kgmol)**2
M_O2 = 32.; #
vm = v*M_O2; #m**3/Kgmol
#p*v = n*R*T
n = 1.
R = 8314.3; #gas constant
p = n*R*T/vm; #N/m**2
print "Pressure using perfect gas equation in N/m**2 : %.1f"%p
#[p+a/vm**2]*[vm-b] = R*T
b = 0.0318;
p = R*T/(vm-b)-a/vm**2; #N/m**2
print "Pressure using Vander Walls equation in N/m**2 : %.1f"%p
# Variables :
m = 22.; #Kg
T = 300.; #K
V = 5.; #m**3
M = 44.; #Kg/Kgmol
a = 362.9; #KNm**4/Kgmol**2
b = 0.0314; #m**3/Kgmol
Rdash = 8314.3; #gas consmath.tant
# Calculations and Results
R = Rdash/M; #Nm/KgK
p = m*R*T/V; #Pa
p = p/10**5; #bar
print "Pressure, when gas behaves like a perfect gas in bar : %.4f"%p
Vdash = V/m*M; #m**3/Kgmole
#[p+a/vm**2]*[vm-b] = R*T
p = Rdash*T/(Vdash-b)-a*10**3/Vdash**2; #N/m**2
print "Pressure umath.sing Vander Walls equation in bar : %.4f"%(p/10**5)
# Variables :
pc = 37.7; #bar
Tc = 132.5; #K
vc = 0.093; #m**3Kgmol
R = 287.; #Nm/KgK
m = 10.; #Kg
T = 300.; #K
V = 0.3; #m**3
# Calculations
a = 27.*R**2*Tc**2./64./pc/10**5;
b = R*Tc/8/pc/10**5; #
#(p+a/V**2)*(V-b) = R*T
p = R*T/(V-b)-a/V**2; #N/m**2
p = p/10**5; #bar
# Results
print "Pressure exerted by air in bar : %.4f"%p
# Variables :
pc = 221.2; #bar
Tc = 374.15+273; #K
p = 100.; #bar
T = 400.+273; #K
R = 462.; #Nm/KgK
# Calculations
#p*v = R*T
v = R*T/p/10**5; #m**3/Kg
print "Specific volume, v by perfect gas equation in m**3/Kg : %.5f"%v
# Results
pr = p/pc;
Tr = T/Tc;
Z = 0.84; #From compressibility chart
v = Z*R*T/p/10**5
print "Specific volume, v by compressibility chart in m**3/Kg : %.5f"%v
# Variables :
pr = 5;
Z = 0.8;
pc = 46.4; #bar
Tc = 191.1; #K
Tr = 1.44; #
# Calculations and Results
p = pr*pc; #bar
print "Pressure in bar : ",p
T = Tr*Tc; #K
print "Temperature in K : ",T
# Variables :
V = 0.01653; #m**3
m = 5.6; #Kg
M = 28. #Kg/Kgmol
p = 200. #bar
Z = 0.605;
Rdash = 8314.3; #J/Kgk
R = Rdash/M; #J/Kgk
# Calculations
#p*V = m*Z*R*T
T = p*10**5*V/m/Z/R; #K
# Results
print "Temperature in K : %.2f"%T
# Variables :
mCO = 0.45; #Kg
mAir = 1; #Kg
V = 0.4; #m**3
T = 15.+273; #K
MCO = 28.; #Kg/Kgmo
MO2 = 32.; #Kg/Kgmol
MN2 = 28.; #Kg/Kgmol
# Calculations
mO2 = 23.3/100*mAir; #Kg
mN2 = 76.7/100*mAir; #Kg
Rdash = 8314.3; #J/Kgk
#p*V = m*Z*R*T
pCO = mCO*Rdash/MCO*T/V/10**5; #bar
pO2 = mO2*Rdash/MO2*T/V/10**5; #bar
pN2 = mN2*Rdash/MN2*T/V/10**5; #bar
# Results
print "Pressure of CO in bar : %.4f"%pCO
print "Pressure of O2 in bar : %.4f"%pO2
print "Pressure of N2 in bar : %.4f"%pN2
p = pCO+pO2+pN2; #bar
print "Total pressure in vessel in bar : %.4f"%p
# Variables :
ma = 0.4; #Kg
mb = 0.8; #Kg
Ma = 44.;
Mb = 29.;
V = 0.4; #m**3
T = 300.; #K
Rdash = 8314.3; #J/Kgk
# Calculations
Ra = Rdash/Ma; #Nm/KgK
Rb = Rdash/Mb; #Nm/KgK
na = ma/Ma; #moles
nb = mb/Mb; #moles
#p*V = n*R*T
pa = na*Rdash/1000*T/V; #bar
pb = nb*Rdash/1000*T/V; #bar
# Results
print "Pressure of container A in KPa : %.2f"%pa
print "Pressure of container B in KPa : %.2f"%pb
p = pa+pb; #Kpa
print "Pressure of mixture in KPa : %.2f"%p
#Ans of Pb is wrong in the book.
# Variables :
Rdash = 8314.3; #J/Kgk
mO2 = 23.15/100;
mN2 = 75.52/100;
mArgon = 1.29/100;
mCO2 = 0.04/100;
MO2 = 32.;
MN2 = 28.;
MArgon = 40.;
MCO2 = 44.;
# Calculations and Results
RO2 = Rdash/MO2; #J/KgK
RN2 = Rdash/MN2; #J/KgK
RArgon = Rdash/MArgon; #J/KgK
RCO2 = Rdash/MCO2; #J/KgK
R = (mO2*RO2+mN2*RN2+RArgon*mArgon+RCO2*mCO2)/(mO2+mN2+mArgon+mCO2); #J/KgK
print "Characteristic gas constant for air in J/KgK : %.2f"%R
M = Rdash/R; #Kg/Kgmol
print "Molecular weight of air in Kg/Kgmol : %.3f"%M
p = 1.013; #bar
nO2 = mO2/MO2; #moles
nCO2 = mCO2/MCO2; #moles
nN2 = mN2/MN2; #moles
nArgon = mArgon/MArgon; #moles
n = nO2+nN2+nArgon+nCO2;
pO2 = nO2/n*p; #bar
pN2 = nN2/n*p; #bar
pArgon = nArgon/n*p; #bar
pCO2 = nCO2/n*p; #bar
print "Pressure of O2 in bar : %.4f"%pO2
print "Pressure of N2 in bar : %.4f"%pN2
print "Pressure of Argon in bar : %.4f"%pArgon
print "Pressure of CO2 in bar : %.5f"%pCO2
# Variables :
yO2 = 0.3;
yN2 = 0.5;
yCO2 = 0.2;
V = 1.; #m**3
T = 27+273; #K
m = 8.; #Kg
MO2 = 32.;
MN2 = 28.;
MCO2 = 44.;
# Calculations and Results
M = 1/(yO2/MO2+yN2/MN2+yCO2/MCO2); #Kg/Kgmol
print "Molecular mass for mixture in Kg/Kgmol : %.3f"%M
Rdash = 8314.3; #J/Kgk
R = Rdash/M; #Nm/KgK
print "Gas consmath.tant R of mixture in Nm/KgK : %.1f"%R
p = m*R*T/V/10**5; #bar
print "Pressure exerted by gases in bar : %.3f"%p
nO2 = yO2/MO2*m; #moles
nCO2 = yCO2/MCO2*m; #moles
nN2 = yN2/MN2*m; #moles
print "Mole fraction of O2(moles) : %.4f"%nO2
print "Mole fraction of N2(moles) : %.4f"%nN2
print "Mole fraction of CO2(moles) : %.4f"%nCO2
# Variables :
mN2 = 4.; #Kg
mO2 = 2.4; #Kg
mCO2 = 1.6; #Kg
MO2 = 32.;
MN2 = 28.;
MCO2 = 44.;
Gamma = 1.4;
# Calculations
#Rdash = Cpdash*(1-1/Gamma)
Rdash = 8.3143; #J/KgK
Cpdash = Rdash*Gamma/(Gamma-1); #KJ/KgmolK
Cvdash = Cpdash/Gamma; #KJ/KgmolK
CpO2 = Cpdash/MO2; #KJ/KgmolK
CpN2 = Cpdash/MN2; #KJ/KgmolK
CpCO2 = Cpdash/MCO2; #KJ/KgmolK
CvO2 = Cvdash/MO2; #KJ/Kg
CvN2 = Cvdash/MN2; #KJ/Kg
CvCO2 = Cvdash/MCO2; #KJ/Kg
# Results
print ("Specific heat of gases : ");
print "For N2, Cp is %.3f"%(CpN2)," KJ/Kg & Cv is %.4f"%CvN2," KJ/Kg."
print "For O2, Cp is %.3f"%CpO2," KJ/Kg & Cv is %.4f"%CvO2," KJ/Kg."
print "For CO2, Cp is %.3f"%CpCO2," KJ/Kg & Cv is %.4f"%CvCO2," KJ/Kg."
Cp = (mO2*CpO2+mN2*CpN2+mCO2*CpCO2)/(mO2+mN2+mCO2); #KJ/KgK
print "Specific heat of mixture, Cp in KJ/KgK : %.5f"%Cp
Cv = (mO2*CvO2+mN2*CvN2+mCO2*CvCO2)/(mO2+mN2+mCO2); #KJ/KgK
print "Specific heat of mixture, Cv in KJ/KgK : %.4f"%Cv