Chapter 9 : Kinetic theory and transport phenomena

Example 9.1 pg : 232

In [2]:
			
# Variables
import math 
N0 = 6.025*10**26
M = 32.
k = 1.38*10**-23
T = 300. 			#K
			
# Calculations
m = M/N0
vavg = math.sqrt(8*k*T/(math.pi*m))
vrms = math.sqrt(3*k*T/m)
vm = math.sqrt(2*k*T/m)
			
# Results
print "Average velocity  =  %d m/sec"%(vavg)
print " RMS velocity  =  %d m/sec"%(vrms)
print " Most probable velocity  =  %.f m/sec"%(vm)

Average velocity  =  445 m/sec
 RMS velocity  =  483 m/sec
 Most probable velocity  =  395 m/sec

Example 9.2 pg : 233

In [4]:
			
# Variables
import math 
T = 300. 			#K
dv = 0.02
vm = 395. 			#m/s
m = 5.32*10**-26 			#kg
k = 1.38*10**-23
vrms = 483. 			#m/s
			
# Calculations
N1 = math.sqrt(2/math.pi) *(m/(k*T))**(3./2) *vm**2 *math.exp(-1) *dv*vm
N2 = math.sqrt(2/math.pi) *(m/(k*T))**(3./2) *vrms**2 *math.exp(-3/2) *dv*vrms
			
# Results
print "Fraction of oxygen molecules at v most probable speed  =  %.4f "%(N1)
print " Fraction of oxygen molecules at v rms speed  =  %.4f "%(N2)

# rounding off error

Fraction of oxygen molecules at v most probable speed  =  0.0167 
 Fraction of oxygen molecules at v rms speed  =  0.0112

Example 9.3 pg : 236

In [5]:
			
# Variables
p = 1.013*10**5 			#N/m**2
k = 1.38*10**-23
T = 300.     	    		#K
v = 445. 	    	    	#m/s
A = 0.001*10**-6 			#m**2
			
# Calculations
n = p/(k*T)
J = n*v/4
escaping = J*A
			
# Results
print "No. of molecules escaping per unit time  =  %.2e mol/sec"%(escaping)

No. of molecules escaping per unit time  =  2.72e+18 mol/sec

Example 9.4 pg : 239

In [6]:
			
# Variables
import math 
d = 3.5*10**-10 			#m
n = 2.45*10**25
			
# Calculations
sig = math.pi*d**2
lambda_ = 1./(math.sqrt(2) *sig*n) 
frac = math.exp(-2)
			
# Results
print "Mean free path  =  %.2e m"%(lambda_)
print " fraction of molecules  =  %.3f"%(frac)

Mean free path  =  7.50e-08 m
 fraction of molecules  =  0.135

Example 9.5 pg : 244

In [7]:
			
# Variables
P = 1. 	    		#atm
T = 300. 			#K
			
# Calculations
cv = 4.97
vavg = 1580.     			#ft/s
sig = 4.13*10**-18 			#ft**2
N0 = 6.025*10**26 *0.4536
K = vavg*3600.*cv/(3*N0*sig)
			
# Results
print "Thermal conductivity   =  %.2e B/hr ft F"%(K)

Thermal conductivity   =  8.35e-03 B/hr ft F

Example 9.6 pg : 245

In [1]:
			
# Variables
m = 5.32*10**-26     			#kg
v = 445.         	    		#m/s
sigma = 3.84*10**-19 			#m**2
			
# Calculations
mu = m*v/(3*sigma)
			
# Results
print "Dynamic viscosity of oxygen  =  %.2e newton sec/m**2"%(mu)

Dynamic viscosity of oxygen  =  2.06e-05 newton sec/m**2