# Chapter 4: Evaluating Properties

## Example 4.01, page: 68

In [5]:
from __future__ import division
import math

#  Initialization  of  Variable
V = 0.5 #volume in m3
P1 = 1  #pressure bar
P2 = 1.5 #pressure bar
vf1 = 1.0432/1000 # m3/kg
vf2=1.0528/1000 # m3/kg
vg1 = 1.694 # in m3/kg
vg2 = 1.159 # in m3/kg
x1 = 0.5

# calculations:
#The specific volume at state 1 and 2
v1 = vf1 + x1*(1.694-vf1)
v2 = v1
#from  table T-3
T1 = 99.63; # in deg C
T2 = 111.4
# the total mass, m
m = V/v1
# the mass of vapor at state 1 and 2
mg1 = x1*m
x2 = (v1-vf2)/(vg2-vf2)
mg2 = x2*m
#if heating continued, from table:
vg3 = 0.8475 #m3/kg
p3 = 2.11 # bar

#Results
print  "a) temperature = ", round(T1,2),"degC at stage 1 and ", round(T2,2),"degC at stage 2"
print  "b) mass  of  vapor =", round(mg1,3)," kg at stage 1 and",round(mg2,3),"kg at stage 2"
print  "c) If heating continued, when the container holds only saturated vapor then pressure =", round(p3,2),"bar"

a) temperature =  99.63 degC at stage 1 and  111.4 degC at stage 2
b) mass  of  vapor = 0.295  kg at stage 1 and 0.431 kg at stage 2
c) If heating continued, when the container holds only saturated vapor then pressure = 2.11 bar


## Example 4.02, page: 69

In [3]:
from __future__ import division
import math

# Initialization  of  Variable
m = 0.1; # mass in lb
P2=20 #pressure in lbf/in2
T2 = 65 # in deg F

# calculations:
# from table, specific volumes
vg1=2.2661
v1 = vg1
#volumes occupied by the refrigerant at states 1 and 2
V1 = m*v1
# from table, specific volume at stage 2
v2=2.6704;
V2 =m*v2

# work
W = P2*(V2-V1)*144/778 # in Btu

#Results
print  "a) volumes occupied by the refrigerant at states 1 and 2 are", round(V1,4),"ft3 and ", round(V2,4),"ft3 respectively"
print  "b) work for the process is", round(W,4),"Btu"

a) volumes occupied by the refrigerant at states 1 and 2 are 0.2266 ft3 and  0.267 ft3 respectively
b) work for the process is 0.1497 Btu


## Example 4.03, page: 73

In [6]:
from __future__ import division
import math

# Initialization  of  Variable
V=10.0# volume ft3
T1 = 212 # indeg F
P2 = 20 # pressure in lbf/in2

#calculations:
# from table, specific volume
v1 = 26.8 # in ft3/lb
u1=1077.6 #btu/lb
v2 = v1
# therefore
u2 = 1161.6 # in Btu/lb
T2 = 445 # deg F
# work
m = V/v1
W = -1*m*(u2-u1)

#Results
print  "a) Temperature is", T2," deg F"
print "b) work during the process is", round(W,1)," Btu"

a) Temperature is 445  deg F
b) work during the process is -31.3  Btu


## Example 4.04, page: 74

In [9]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 10  #pressure bar
T1 = 400 # temp in deg C
T2 = 150 #  temp in deg C
vf3 = 1.0905E-3 # in m3/kg
vg3 = 0.3928 # in m3/kg

# calculations:
#From Table, specific volume at state 1 and 2
v1 = 0.3066 #in m3/kg
u1 = 2957.3 # in kJ/kg
v2 = 0.1944 # m3/kg
#work
Wm = P1*(v2-v1)*10**2

#heat transfer
v3 = v2
x3 = (v3 - vf3)/(vg3 - vf3)
#from Table
uf3 = 631.68 # kJ/kg
ug3 = 2559.5 #kJ/kg
u3 = uf3 + x3*(ug3-uf3)

Qm = u3 - u1 + Wm

#Results
print  "b)Work =",round(Wm,1),"kJ/kg"
print  "c)Heat Transfer =",round(Qm,1),"kJ/kg"

b)Work = -112.2 kJ/kg
c)Heat Transfer = -1486.4 kJ/kg


## Example 4.06, page: 80

In [10]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 20E6 # pressure pa
T1 = 520 # temp in deg C
T2 = 400  #temp deg C
M = 18.02 #molar mass in kg/kmol
Rbar = 8314 #in Nm/kmol-K

#calculations:
R = Rbar/M
#From Table T-1
Tc = 647.3 #in K
Pc = 22.09E6 # in Pa
#reduced Temp
Tr1 = (T1 + 273)/Tc
#reduced Pressure
Pr1 = P1/Pc
#compressibility factor
Z = 0.83
#specific volume
v1 = Z*Rbar*(T1+273)/(M*P1)

#Constant refuced value of spec vol
vr = v1*Pc/(R*Tc)
#at state 2, reduced Temp
Tr2 = (T2+273)/Tc
# from compressibility chart
Pr2 = 0.69

P2 = Pc*Pr2

#Results
print  "a) specific volume of the water vapor at initial stage is", round(v1,4),"m3/kg"
print  "b) Pressure at final stage is", round(P2/1E6,2),"Mpa"

a) specific volume of the water vapor at initial stage is 0.0152 m3/kg
b) Pressure at final stage is 15.24 Mpa


## Example 4.07, page: 82

In [11]:
from __future__ import division
import math

# Initialization  of  Variable
m = 1 #mass in lb
P1 = 1 # atm
T1 = 540 # in deg R
P2 = 2 # in Atm
R = 1545/28.97

#calculations:
#Using pv=RT, the temperature at state 2 is
T2 = P2*T1/P1

#Since pv=RT, the specific volume at state 3 is
v3 = R*T2/(P1*14.7*144)

#Results
print  "b)temperature  at state 2 is", round(T2,0),"degR"
print  "c)specific  volume at state 3 is ", round(v3,1) ,"ft3/lb"

b)temperature  at state 2 is 1080.0 degR
c)specific  volume at state 3 is  27.2 ft3/lb


## Example 4.08, page: 86

In [12]:
from __future__ import division
import math

# Initialization  of  Variable
m = 2 # mass lb
T1 = 540 #in degR
P1 = 1 # in atm
T2 = 840 #in degR
P2 = 6 # in atm
Q = -20 # in Btu

# calculations:
#From Table T-9E
u1 = 92.04 # in Btu/lb
u2 = 143.98 # in Btu/lb
#work
W = Q - m*(u2-u1)

#Results
print  "work  done  during the process is", round(W,1),"Btu"

work  done  during the process is -123.9 Btu


## Example 4.10, page: 87

In [13]:
from __future__ import division
import math

# Initialization  of  Variable
m1co = 2 #kg
T1co = 77 # degC
P1co = 0.7 #bar

m2co = 8 #kg
T2co = 27 # degC
P2co = 1.2 #bar

Tf = 42 # degC
Cv = 0.745 #kJ/kg-K

#calculations:
#final pressure
Pf = (m1co + m2co)*Tf/((m1co*T1co/P1co) + (m2co*T2co/P2co))

#heat
Q = m1co*Cv*(Tf-T1co) + m2co*Cv*(Tf-T2co)

#Results
print  "a)final  pressure is", round(Pf,2),"bar"
print  "b)heat  transfer  for the process is", round(Q,2),"kJ"

a)final  pressure is 1.05 bar
b)heat  transfer  for the process is 37.25 kJ


## Example 4.11, page: 90

In [14]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 1 #atm
T1 = 70 # degF
P2 = 5 #atm
n = 1.3
R = 1.986/28.97 #Btu/lb-degR

#calculations:
#Temp at 1 in rankine
T1r = (((T1 - 32)*5/9)+273)*1.8
#temp at 2 in Rankine
T2r = T1r*(P2/P1)**((n-1)/n)

#work per unit mass
Wm = R*(T2r-T1r)/(1-n)
#heat per unit mass
#from table T-9E
u2 = 131.88 #Btu/lb
u1 = 90.33 #Btu/lb
Qm = Wm + (u2-u1)

#Results
print  "Work per  unit mass is", round(Wm,2),"Btu/lb"
print  "heat transfer per unit mass is",round(Qm,2),"Btu/lb"

Work per  unit mass is -54.41 Btu/lb