Chapter11 KineticTheory

Example 11.1, Page no.45

In [7]:
import math
from math import sqrt
from math import pi
#initialisation of variables
R=8.31*10 # ergs moleˆ−1 Kˆ−1 
M=2.016 #gms 
T=0 #C 
#CALCULATIONS 
vp=sqrt(2*R*(273+T)/M)
v=sqrt(8*R*(273+T))/(pi*M)
vr=sqrt(3*R*(273+T)/M) 
#RESULTS
vp=round(vp,2)
v=round(v,2)
vr=round(vr,2)
print 'most probabale velocity=',vp,'cm secˆ−1'
print 'arthmetic mean velocity=',v,'cm secˆ−1'
print 'root mean square velocity=',vr,'cm sec ˆ−1'

most probabale velocity= 150.02 cm secˆ−1
arthmetic mean velocity= 67.26 cm secˆ−1
root mean square velocity= 183.74 cm sec ˆ−1

Example 11.2, Page no.45

In [8]:
import math
from math import sqrt
from math import pi
#initialisation of variables
R=8.31*10**7 # ergs moleˆ−1 Kˆ−1
M=9.013 #mg
T=1457 #K
d=0.318 #cm
t=60.1 #min
m=9.54 #mg
g=980 # cmsecˆ−2 
D=13.6 #g/ cc 
p=76 #cm atmˆ−1
#CALCULATIONS
P=sqrt(2*pi*R*T/M)*(m*10**-3/(pi*(d/2)**2*t*60*p*D* g))
#RESULTS
print 'vapour pressure=',format(P, '.8f'),'atm'

vapour pressure= 0.00000955 atm

Example 11.3, Page no.46

In [9]:
import math
from math import sqrt
#initialisation of variables
M1=238.0 #gms
M2=235.0 #gms 
A=6.0 
N=19.0 
#CALCULATIONS 
r=sqrt((M1+A*N)/(M2+A*N)) 
#RESULTS
r=round(r,3)
print 'ratio of rates=',r

ratio of rates= 1.004

Example 11.4, Page no.46

In [9]:
import math
from math import sqrt,pi
#initialisation of variables
s=3.61*10** -8 #cm 
v=4.44*10**4 #cm/sec 
n=2.46*10**19 # molecules 
N=6.02*10**23 # molecules 
Z1=13.6*10**16 # collisions cmˆ−3 secˆ−1 
N=6*10**23 # molecules
#CALCULATIONS
Z=sqrt(2)*pi*s**2*v*n**2*10**3/(2*N)
Z2= Z1*10**3/N
#RESULTS
Z=Z/(10**6)
Z=round(Z,1)
print 'Z=',Z,'M moles of collisions litreˆ−1 secˆ−1'
print 'Z2=',format(Z2, '.8f'),'moles of collisions litre ˆ−1 sec ˆ−1'

Z= 129.6 M moles of collisions litreˆ−1 secˆ−1
Z2= 0.00022667 moles of collisions litre ˆ−1 sec ˆ−1

Example 11.5, Page no.47

In [16]:
import math
#initialisation of variables
from math import sqrt
from math import pi
n=2.46*10**19 # molecules cmˆ−3 
n1=3.24*10**13 # molecules cmˆ−3 
l=3.61*10**-8 
#CALCULATIONS 
L=(sqrt(2)*pi*l**2*n)**-1 
L1=(sqrt(2)*pi*l**2*n1)**-1 
#RESULTS
L1=round(L1,2)
print 'mean free path=',format(L, '.8f'),'cm'
print 'mean free path=',L1,'cm'
print 'ANSWER GIVEN IN THE TEXTBOOK IS WRONG'

mean free path= 0.00000702 cm
mean free path= 5.33 cm
ANSWER GIVEN IN THE TEXTBOOK IS WRONG