import math
T1 = 37.0 # Final water temperature in degree Celsius
T2 = 35.0 # Initial water temperature in degree Celsius
m = 1.0 # Mass of water in kg
cv = 4.187 # Specific heat capacity of water in kJ/kgK
print "\n Example 7.1"
S = m*cv*math.log((T1+273)/(T2+273)) # Change in entropy of the water
print "\n Change in entropy of the water is ",round(S,4) ," kJ/K"
#The answer provided in the textbook is wrong
import math
# Part (a)
T1 = 273 # Initial temperature of water in Kelvin
T2 = 373 # Temperature of heat reservoir in Kelvin
m = 1 # Mass of water in kg
cv = 4.187 # Specific heat capacity of water
print "\n Example 7.2"
Ss = m*cv*math.log(T2/T1) # entropy change of water
Q = m*cv*(T2-T1) # Heat transfer
Sr = -(Q/T2) # Entropy change of universe
S = Ss+Sr # Total entropy change
print "\n The entropy change of the universe is ",S ," kJ/K"
# Part (b)
T3 = 323 # Temperature of intermediate reservoir in K
Sw = m*cv*(math.log(T3/T1)+math.log(T2/T3)) # entropy change of water
Sr1 = -m*cv*(T3-T1)/T3 # Entropy change of universe
Sr2 = -m*cv*(T2-T3)/T2 # Entropy change of universe
Su = Sw+Sr1+Sr2 # Total entropy change
print "\n The entropy change of the universe is ",Su ," kJ/K"
#The answers vary due to round off error
import math
m = 1 # Mass of ice in kg
T1 = -5 # Initial temperature of ice in degree Celsius
T2 = 20# Atmospheric temperature in degree Celsius
T0 = 0# Phase change temperature of ice in degree Celsius
cp = 2.093 # Specific heat capacity of ice in kJ/kgK
cv = 4.187 # Specific heat capacity of water in kJ/kgK
lf = 333.3 # Latent heat of fusion in kJ/kgK
print "\n Example 7.3"
Q = m*cp*(T0-T1)+1*333.3+m*cv*(T2-T0) # Net heat transfer
Sa = -Q/(T2+273) # Entropy change of surrounding
Ss1 = m*cp*math.log((T0+273)/(T1+273)) # entropy change during
Ss2 = lf/(T0+273) # Entropy change during phase change
Ss3 = m*cv*math.log((T2+273)/(T0+273)) # entropy change of water
St = Ss1+Ss2+Ss3 # total entropy change of ice to convert into water at atmospheric temperature
Su = St+Sa # Net entropy change of universe
print "\n The entropy change of the universe is ",Su ," kJ/K"
#The answer provided in the textbook is wrong
# Part (b)
S = St # Entropy change of system
Wmin = (T2+273)*(S)-Q # minimum work required
print "\n The minimum work required is ",Wmin ," kJ"
#The answers vary due to round off error
import math
P1 = 0.5 # Initial pressure in MPa
V1 = 0.2 # Initial volume in m**3
V2 = 0.05 # Final volume in m**3
n = 1.3 # Polytropic index
from scipy import integrate
print "\n Example 7.7"
P2 = P1*(V1/V2)**n
def f(p):
y = ((P1*V1**n)/p)**(1/n)
return y
H, err = integrate.quad(f,P1,P2) # H = H2-H1
U = H-(P2*V2-P1*V1)
W12 = -U
print "\n Change in enthalpy is ",round(H*1e3,2)," kJ"
print "\n Change in internal energy is ",round(U*1000,2)," kJ"
print "\n The change in entropy and heat transfer are is ",0 ," kJ"
print "\n The work transfer during the process is ",round(W12*1000,2) ," kJ"
#The answers vary due to round off error
import math
from scipy import integrate
Pa = 130.0 # Pressure at station A in kPa
Pb = 100.0# Pressure at station B in kPa
Ta = 50.0 # Temperature at station A in degree Celsius
Tb = 13.0# Temperature at station B in degree Celsius
cp = 1.005 # Specific heat capacity of air in kJ/kgK
x= lambda t:cp/t
y= lambda p:0.287/p
print "\n Example 7.8"
Sb,error = integrate.quad(x,Ta,Tb)#-
Sa,eror=integrate.quad(y,Pa,Pb)
Ss=Sb-Sa
Ssur=0
Su = Ss+Ssur
print "\n Change in the entropy of the universe is ",Su ," kJ/Kg K"
#The answers given in the book is wrong
print "\n As the change in entropy of the universe in the process A-B is negative \n so the flow must be from B-A"
import math
T1 = 300.0 # Inlet temperature of air in K
T2 = 330.0 # Exit temperature of first air stream in K
T3 = 270.0 # Exit temperature of second air stream in K
P1 = 4.0 # Pressure of inlet air stream in bar
P2 =1.0 # Pressure of first exit air stream in bar
P3 =1.0 # Pressure of second exit air stream in bar
cp = 1.0005 # Specific heat capacity of air in kJ/kgK
R = 0.287 # Gas constant
print "\n Example 7.9"
S21 = cp*math.log(T2/T1)-R*math.log(P2/P1) # Entropy generation
S31 = cp*math.log(T3/T1)-R*math.log(P3/P1) # Entropy generation
Sgen = (1.0*S21) + (1.0*S31) # Total entropy generation
print "\n The entropy generated during the process is ",Sgen ," kW/K"
#The answers vary due to round off error
print "\n As the entropy generated is positive so such device is possible"
import math
A = 5*7 # Area of wall in m**2
k = 0.71# Thermal conductivity in W/mK
L = 0.32 # Thickness of wall in m
Ti = 21 # Room temperature in degree Celsius
To = 6 # Surrounding temperature in degree Celsius
print "\n Example 7.10"
Q = k*A*(Ti-To)/L # Heat transfer
Sgen_wall = Q/(To+273) - Q/(Ti+273) # Entropy generation in wall
print "\n The rate of heat transfer through the wall is ",Q ," W"
print "\n The rate of entropy through the wall is ",Sgen_wall ," W/K"
Tr = 27 # Inner surface temperature of wall in degree Celsius
Ts = 2 # Outer surface temperature of wall in degree Celsius
Sgen_total = Q/(Ts+273)-Q/(Tr+273) # Total entropy generation in process
print "\n The rate of total entropy generation with this heat transfer process is ",Sgen_total ," W/K"