Chapter 7 : Entropy

Example 7.2 Page No : Page No : 172

In [1]:
import math 

# Variables
v1 = 0.05;		    	# in m**3
v2 = 8. * v1;			# in m**3
T1 = 280.;		    	# in °C
T1 = T1 + 273;			# in K
T2 = 25.;		        # in °C
T2 = T2 + 273;			# in K
p1 = 8.;	        		# in bar
C_p = 1.005;			# in kJ/kgK
C_v = 0.712;			# in kJ/kgK

# Calculations
R = C_p - C_v;			# in kJ/kgK
del_phi = (R * ( math.log(v2/v1)) ) + (C_v * (math.log(T2/T1)) );			# in kJ/kgK

# Results
print "The change in entrophy of air during the process in kJ/kgK is : %.3f"%del_phi

The change in entrophy of air during the process in kJ/kgK is : 0.169

Example 7.3 Page No : 172

In [2]:
import math 

# Variables
m = 5.;      			# in kg
T1 = 50.;	    		# in °C
T1 = T1 + 273;			# in K
T2 = 250.;			    # in °C
T2 = T2 + 273;	    	# in K
C_p = 1.0;
C_v = 0.72;
T3 = 50.;   			# in °C
T3 = T3 + 273;			# in K

# Calculations
del_phi = m * C_p * (math.log(T2/T1));			# in kJ/ K (this is increase in entrophy)
del_phi1 = m * C_v * (math.log(T3/T2));			# in kJ/K (this is decrease in entrophy)
phi_net = del_phi - abs(del_phi1);			    # in kJ/K

# Results
print  "net change in entrophy in kJ/K is : %.3f"%phi_net

net change in entrophy in kJ/K is : 0.675

Example 7.6 Page No : 174

In [4]:
# Variables
Q1 = 1600.;			# in kJ
Q2 = 1600.;			# in kJ
T1 = 800.;			# in K
T2 = 127.;			# in °C

# Calculations
T2 = T2 + 273;			# in K
d1_phi = Q1/T1;			# in kJ per K
d2_phi = Q2/T2;			# in kJ per K
net_phi = d2_phi - d1_phi;			# in kJ per K

# Results
print "entrophy generated during the process in kJ/K is : ",net_phi

entrophy generated during the process in kJ/K is :  2.0

Example 7.8 Page No : 175

In [1]:
import math 

# Variables
T_A = 50.+273;			# in K
T_B = 13.+273;			# in K
P_A = 130.;			# in kPa
P_B = 100.;			# in kPa
Cp = 1.005;			# in kJ/kg-K
pvByT = 0.287;			# p in kPa, v in m**3/kg, T in K

# Calculations
del_S_system = Cp*math.log(T_B/T_A)-pvByT*math.log(P_B/P_A);			# in kJ/kg-K
del_S_surrounding = 0;
del_S_universe = del_S_system+del_S_surrounding;			# in kJ/kg-K

# Results
print  "change in entropy in kJ/kg-K is : %.3f"%del_S_universe
print ("But a negative change in entropy is not possible,");
print ("therefore the flow of air must be from B to A")

change in entropy in kJ/kg-K is : -0.047
But a negative change in entropy is not possible,
therefore the flow of air must be from B to A

Example 7.9 Page No : 176

In [4]:
import math 

# Variables
m = 5.	    		# in kg
s= 4.18 
T1 = 0.	    		# in °C
T2 = 20.			# in °C
dt = T2 - T1;			# in °C
Q = m * s * dt;			# in kJ
L = 335.;			# in kJ/kg

# Calculations
# Q = m_i * l
m_i = Q/L;			# in kg
T1 = T1 + 273;			# in K
T2 = T2 + 273;			# in K
del_S = ((m_i * L)/T1) - (m * s * (math.log(T1/T2)));			# in kJ per K

# Results
print  "change in entropy of the adiabatic system in kJ/K is %.3f"%del_S

change in entropy of the adiabatic system in kJ/K is 3.009

Example 7.11 Page No : 177

In [1]:
import math 

# Variables
p1 = 1. * 10**5;			# in N/m**2
C_p = 1.005;			# in kJ/kg k
R = 287.;			# in j/kg k
T1 = 290.;			# in K
T2 = 580.;			# in K
v1 = 1.;			# in m**3

# Calculations
m = (p1 * v1)/(R * T1);			# in kg
Q = m * R * (T2-T1);			# in J
Q = Q * 10**-3;			# in kJ
del_phi = m * C_p * (math.log(T2/T1));			# in kJ per K
R = R * 10**-3;			# in kJ/kg K
C_v = C_p - R;			# in kJ/kg k
del1_phi = m * C_v * (math.log(T1/T2));			# in kJ/K
net_phi = del_phi + del1_phi;			# in kJ/K

# Results
print "Over all change in entrophy in kJ/K is : %.4f"%net_phi

# rounding off error

Over all change in entrophy in kJ/K is : 0.2390