from __future__ import division
from sympy.mpmath import quad
print "Example: 2.1 - Page: 39\n\n"
# Solution
#*****Data*****#
#deff('[E] = f1(T)','E = 50 + 25*T + 0.05*T**2')## [J]
#deff('[Q] = f2(T)','Q = 4000 + 10*T')## [J]
def f1(T):
E = 50 + 25*T + 0.05*T**2
return E
def f2(T):
Q = 4000 + 10*T
return Q
Ti = 400## [K]
Tf = 800## [K]
#*************#
# From the first law of thermodynamics:
# W = Q - delta_E
# W = f2 -f1
W = quad(lambda T:(4000 + 10*T) - (50 + (25*T) + (0.05*T**2)),[Ti,Tf])#
print "The work done during the process is %.2f kJ\n"%(W/1000)#
from __future__ import division
print "Example: 2.2 - Page: 40\n\n"
# Solution
#*****Data*****#
U1 = 1000## [kJ]
Q = -600# # [kJ]
W = -100## [kJ]
#************#
# The system is considered to be a closed system. No mass transfer takes place across the system. The tank is rigid.
# So, the kinetic and the potential energies is zero.
# Therefore:
# delta_E = delta_U + delta_PE + delta_KE
# delta_E = delta_U
# From the first law of thermodynamics:
# Q = delta_U + W
# delta_U = Q - W
# U2 - U1 = Q - W
U2 = U1 + Q - W## [kJ]
print "The final internal energy of the fluid is %d kJ\n"%(U2)#
from __future__ import division
print "Example: 2.3 - Page: 40\n\n"
# Solution
#*****Data*****#
W = -3## [hp]
Q = -4000## [kJ/h]
#**************#
# The work done by the stirrer on the system is given by
W = W*745.7## [W]
# The amount of heat transferred to the suroundings can be expressed in terms of J/s:
Q = Q*1000/3600## [J/s]
# From the first law of thermodynamics:
# Q = delta_U - W
delta_U = Q - W## [J/s]
print "The change in the internal energy of the system would be %.2f J/s\n"%(delta_U)#
from __future__ import division
print "Example: 2.4 - Page: 41\n\n"
# Solution
#*****Data*****#
# From Fig. 2.4 (Page: 41)
# For process A-1-B:
Q1 = 60## [kJ]
W1 = 35## [kJ]
# For process A-2-B:
W2 = 50## [kJ]
# For process B-3-A:
W3 = -70## [kJ]
#************#
# For process A-1-B:
# The internal energy of the process A-1-B can be estimated as:
# Q = delta_U + W
delta_U = Q1 - W1## [kJ]
# For process A-2-B:
Q2 = delta_U + W2## [kJ]
# For process B-3-A:
Q3 = -delta_U + W3## [kJ]
print "The amount of heat transferred from the system to the surroundings during process B-3-A is %d kJ\n"%(-Q3)#
from __future__ import division
print "Example: 2.5 - Page: 41\n\n"
# Solution
#*****Data*****#
# For constant pressure process 1-2:
W12 = -100## [kJ]
Q12 = -50## [kJ]
# For constant volume process 2-3:
Q23 = 80## [kJ]
# process 3-1: Adiabatic process
#**************#
# The internal energy of process 1-2 can be calculated as:
delta_U12 = Q12 - W12## [kJ]
print "Change in Internal Energy for process 1-2 is %d kJ\n"%(delta_U12)#
# For the process 2-3:
# As the process is constant volume process:
W23 = 0## [kJ]
delta_U23 = Q23 - W23## [kJ]
print "Change in Internal Energy for process 2-3 is %d kJ\n"%(delta_U23)#
# For process 3-1:
# Since the process is adiabatic, ther is no heat transfer between the system and the surrounding.
Q31 = 0## [kJ]
# For a cyclic process, the internal energy change is zero.
# delta_U12 + delta_U23 + delta_U31 = 0
delta_U31 = -(delta_U12 + delta_U23)## [kJ]
# Putting the value of delta_U31:
W31 = Q31 - delta_U31## [kJ]
print "Change in Internal Energy for process 3-1 is %d kJ\n"%(delta_U31)#
print "The work done during the adiabatic process is %d kJ\n"%(W31)#
from __future__ import division
print "Example: 2.6 - Page: 44\n\n"
# Solution
#*****Data*****#
m = 1## [kg]
Temp = 373## [K]
P = 101325## [N/square m]
V_Liquid = 1.04*10**(-3)## [cubic m/kg]
V_Vapour = 1.673## [cubic m/kg]
Q = 2257## [kJ]
#**************#
# Work done due to expansion:
Wexpansion = P*(V_Vapour - V_Liquid)## [N-m]
deltaU = Q - Wexpansion/1000## [kJ]
deltaH = deltaU + Wexpansion/1000## [kJ]
print "Change in Internal Energy is %.2f kJ\n"%(deltaU)#
print "Change in enthalpy is %d kJ\n"%(deltaH)#
from __future__ import division
print "Example: 2.7 - Page: 45\n\n"
# Solution
#*****Data*****#
n = 1## [mol]
Temp = 353## [K]
P = 1## [atm]
Hv = 380## [J/g]
Mwt = 78## [g/mol]
R = 8.314## [J/K mol]
#*************#
Q = Hv*Mwt## [J/mol]
# Since Vv >> Vl:
# P*(Vv - Vl) = P*Vv =n*R*Temp
Wexpansion = n*R*Temp## [J]
# By first law of thermodynamics:
deltaU = Q - Wexpansion## [J]
deltaH = deltaU + Wexpansion## [J]
print "Change in Internal Energy is %.2f J\n"%(deltaU)#
print "Change in Enthalpy is %d J\n"%(deltaH)#
print "Amount of Heat supplied is %d J\n"%(Q)#
print "Work done is %.2f J\n"%(Wexpansion)#
from __future__ import division
print "Example: 2.8 - Page: 45\n\n"
# Solution
#*****Data*****#
deltaU = 200## [cal]
Vinit = 10## [L]
Vfinal = 50## [L]
#deff('[P] = f(V)','P = 10/V')#
def f(V):
P=10/V
return P
#**************#
# By definition of enthalpy:
# deltaQ = deltaU + PdV
deltaQ = deltaU + quad(f,[Vinit,Vfinal])*24.2## [cal]
print "Change in enthalpy is %.2f cal\n"%(deltaQ)#
from __future__ import division
print "Example: 2.9 - Page: 48\n\n"
# Solution
#*****Data*****#
m_water = 1## [kg]
Cv = 4.18## [kJ/kg K]
m_stirrer = 40## [kg]
h = 25## [m]
g = 9.81## [m/square s]
#***************#
# Since the system is thermally insulated:
# Q = 0
# From the first law of thermodynamics:
# dQ = dE + dW
# As E = U + Ek +Ep and Ek = Ep = 0
# dQ = dU + dW
dT = g*h/Cv## [K]
print "Rise in Temperature is %.2f K\n"%(dT)#
from __future__ import division
print "Example: 2.10 - Page: 53\n\n"
# Solution
#*****Data*****#
T1 = 300## [K]
V1 = 30## [L]
V2 = 3## [L]
Cv = 5## [cal/mol]
R = 2## [cal/K mol]
#*************#
Cp = Cv + R## [cal/mol]
gama = Cp/Cv#
# The relation between temperature and volume of ideal gas undergoing adiabatic change is given by:
# (T2/T1) = (V1/V2)**(gama - 1)
T2 = T1 * (V1/V2)**(gama - 1)## [K]
print "The final temperature is %.1f K\n"%(T2)#
from __future__ import division
print "Example: 2.11 - Page: 53\n\n"
# Solution
#*****Data*****#
n = 2## [mol]
T1 = 293## [K]
P1 = 15##[atm]
P2 = 5## [atm]
Cp = 8.58## [cal/degree mol]
#**************#
R = 2## [cal/degree mol]
Cv = Cp - R## [cal /degree mol]
gama = Cp/Cv#
R = 0.082## [L atm/degree K]
# Since the gas is ideal:
V1 = n*R*T1/P1## [L]
# Under adiabatic conditions:
# (V2/V1) = (P1/P2)**(1/gama)
V2 = V1*(P1/P2)**(1/gama)## [L]
print "The final volme is %.2f L\n"%(V2)#
# To determine the final temperature:
# (T2/T1) = (V1/V2)**(gama - 1)#
T2 = T1*(V1/V2)**(gama - 1)## [K]
print "The final temperature is %.2f K\n"%(T2)#
# Adiabatic Work done can be calculated as:
W = (P1*V1 - P2*V2)/(gama - 1)#
print "Adiabatic work done is %.2f L-atm\n"%(W)#
from __future__ import division
from math import log
print "Example: 2.12 - Page: 57\n\n"
# Solution
#*****Data*****#
m = 1## [kg]
P1 = 8## [atm]
T1 = 50 + 273## [K]
# V1 = V## [L]
# V2 = 5V## [L]
V1_by_V2 = 1/5#
gama = 1.4#
R = 0.082## [L-atm]
#***************#
# Adiabatic process:
print "Adiabatic Process \n"
P2 = P1*V1_by_V2**gama## [atm]
print "Final Pressure is %.2f atm\n"%(P2)#
T2 = T1*V1_by_V2**(gama - 1)## [K]
print "Final Temperature is %f K\n"%(T2)#
Wad = R*(T2 - T1)/(1 - gama)## [L-atm]
print "Adiabatic Work done is %.3f L-atm\n"%(Wad)#
print "\n"
# Isothermal Process:
print "Isothermal Process\n"
# In an isothermal Process, the temperature remans constant:
T2 = T1## [K]
print "Final temperature is %d K\n"%(T2)#
# From the ideal gas:
# (P2*V2/T2) = (P1*V1/T1)
# Since T2 = T1
# P2*V2 = P1*V1
P2 = P1*V1_by_V2## [atm]
print "Final pressure is %.1f atm\n"%(P2)#
W = R*T1*log(1/V1_by_V2)## [L-atm]
print "Work done during the isothermal process is %.2f L-atm\n"%(W)#
from __future__ import division
print "Example: 2.13 - Page: 58\n\n"
# Solution
#*****Data*****#
m = 5## [kg]
M = 29## [kg/mol]
T1 = 37 + 273## [K]
P1 = 101.33## [kPa]
T2 = 237 + 273## [K]
Cp = 29.1## [J/mol K]
Cv = 20.78## [J/mol K]
R = 8.314## [J/K mol]
#*****************#
n = m/M#
# From ideal gas equation:
V1 = n*R*T1/P1## [cubic m]
# Isochoric Process:
print "Isochoric Process\n"
# Volume = constant
V2 = V1## [cubic m]
deltaU = n*Cv*(T2 - T1)## [kJ]
# Since Volume is constant
W = 0#
Q = deltaU + W## [kJ]
# deltaH = deltaU + P*deltaV
# deltaH = deltaU + n*R*deltaT
deltaH = deltaU + n*R*(T2 - T1)## [kJ]
print "Change in Internal Energy is %.2f kJ\n"%(deltaU)#
print "Heat Supplied is %.2f kJ\n"%(Q)#
print "Work done is %d kJ\n"%(W)#
print "Change in Enthalpy is %.2f kJ\n"%(deltaH)#
print "\n"
# Isobaric Process
print "Isobaric Process\n"
# Since Pressure is constant.
P2 = P1## [kPa]
deltaH = n*Cp*(T2 - T1)## [kJ]
Qp = deltaH## [kJ]
# deltaU = deltaH - P*deltaV
# From ideal gas equation:
deltaU = deltaH - n*R*(T2 - T1)## [kJ]
W = Qp - deltaU## [kJ]
print "Change in Internal Energy is %.2f kJ\n"%(deltaU)#
print "Heat Supplied is %.2f kJ\n"%(Qp)#
print "Work done is %.2f kJ\n"%(W)#
print "Change in Enthalpy is %.2f kJ\n"%(deltaH)#
from __future__ import division
from math import log10
print "Example: 2.14 - Page: 60\n\n"
# Solution
#*****Data*****#
n = 1## [mol]
T1 = 610## [K]
P1 = 10**6## [N/square m]
T2 = 310## [K]
P2 = 10**5## [N/square m]
Cv = 20.78## [J/mol K]
#*************#
R = 8.314## [J/K mol]
# Step 1: Isothermal Expansion Of Ideal Gas:
print "Step 1: Isothermal Expansion Of Ideal Gas\n"
T1 = 610## [K]
P1 = 10**6## [N/square m]
P2 = 10**5## [N/square m]
# Work done:
W1 = 2.303*n*R*T1*log10(P1/P2)## [J/mol]
# For isothermal expansion:
delta_E1 = 0## [J/mol]
# From first law of thermodynamics:
Q1 = delta_E1 + W1## [J/mol]
print "delta_E for Step 1 is %d J/mol\n"%(delta_E1)#
print "Q for step 1 is %.2f J/mol\n"%(Q1)#
print "W for step 1 is %.2f J/mol\n"%(W1)#
print "\n"
# Step 2: Adiabatic Expansion of ideal gas:
print "Step 2: Adiabatic Expansion of ideal gas\n"
Q2 = 0## [J/mol]
delta_E2 = Cv*(T2 - T1)## [J/mol]
# From first law of thermodynamics:
W2 = Q2 - delta_E2## [J/mol]
print "delta_E for Step 2 is %d J/mol\n"%(delta_E2)#
print "Q for step 2 is %.2f J/mol\n"%(Q2)#
print "W for step 2 is %.2f J/mol\n"%(W2)#
print "\n"
# Step 3: Isothermal Compression Of Ideal Gas:
print "Step 3: Isothermal Compression Of Ideal Gas\n"
T2 = 310## [K]
P1 = 10**5## [N/square m]
P2 = 10**6## [N/square m]
# Work done:
W3 = 2.303*n*R*T2*log10(P1/P2)## [J/mol]
# For isothermal expansion:
delta_E3 = 0## [J/mol]
# From first law of thermodynamics:
Q3 = delta_E3 + W3## [J/mol]
print "delta_E for Step 3 is %d J/mol\n"%(delta_E3)#
print "Q for step 3 is %.2f J/mol\n"%(Q3)#
print "W for step 3 is %.2f J/mol\n"%(W3)#
print "\n"
# Step 4: Adiabatic Compression of ideal gas:
print "Step 4: Adiabatic Compression of ideal gas\n"
T1 = 310## [K]
T2 = 610## [K]
Q4 = 0## [J/mol]
delta_E4 = Cv*(T2 - T1)## [J/mol]
# From first law of thermodynamics:
W4 = Q4 - delta_E4## [J/mol]
print "delta_E for Step 4 is %d J/mol\n"%(delta_E4)#
print "Q for step 4 is %.2f J/mol\n"%(Q4)#
print "W for step 4 is %.2f J/mol\n"%(W4)#
print "\n"
# Net work done for the complete cycle:
W = W1 + W2 + W3 + W4## [J/mol]
print "Net Work done for the complete cycle is %.2f J/mol\n"%(W)#
# The efficiency of the cycle is given by:
eta = 1- T1/T2#
print "The efficiency of the cycle is %.2f\n"%(eta)#
print "Example: 2.15 - Page: 61\n\n"
# Mathematics is involved in proving but just that no numerical computations are involved.
# For prove refer to this example 2.15 on page number 61 of the book.
print " Mathematics is involved in proving but just that no numerical computations are involved.\n\n"
print " For prove refer to this example 2.15 on page 61 of the book."
from __future__ import division
print "Example: 2.16 - Page: 62\n\n"
# Solution
#*****Data*****#
P1 = 1## [bar]
T1 = 300##[K]
V1 = 24.92## [cubic m/kmol]
P2 = 10## [bar]
T2 = 300## [K]
Cp = 29.10## [kJ/kmol K]
Cv = 20.78## [kJ/kmol K]
R = 8.314## [J/mol K]
#**************#
# Basis: 1 kmol of ideal gas:
n = 1#
V2 = P1*V1/P2## [cubic m]
# First Process:
print "First Process\n"
# In the first step of the first process, the cooling of ga takes place at constant pressure.
# Here the volume is reduced appreciably and consequently the temperature decreases.
T_prime = T1*V2/V1## [K]
# Heat Requirement:
Q1 = n*Cp*(T_prime - T1)## [kJ]
deltaH1 = Q1## [kJ]
deltaU1 = deltaH1 - P1*(V2 - V1)## [kJ]
# In the second step, the gas is heated at constant Volume:
# V = constant
Q2 = n*Cv*(T2 - T_prime)## [kJ]
deltaU2 = Q2## [kJ]
deltaH2 = n*R*(T2 - T_prime)## [kJ]
deltaU = deltaU1 + deltaU2## [kJ]
deltaH = deltaH1 + deltaH2## [kJ]
Q = Q1 + Q2## [kJ]
print "Change in Internal Energy is %.2f kJ\n"%(deltaU)#
print "Change in Enthalpy is %.2f kJ\n"%(deltaH)#
print "Heat Requirement is %.2f kJ\n"%(Q)#
print "\n"
# Second Process:
print "Second Process\n"
# In the first step of the second process, the gas is heated at constant volume.
T_prime = T1*P2/P1## [K]
# Heat Requirement:
Q1 = n*Cv*(T_prime - T1)## [kJ]
deltaU1 = Q1## [kJ]
deltaH1 = n*R*(T_prime - T1)## [kJ]
# In the second step, the gas is cooled at constant presure:
# V = constant
Q2 = n*Cp*(T2 - T_prime)## [kJ]
deltaH2 = Q2## [kJ]
deltaU2 = deltaH2 - P1*(V2 - V1)## [kJ]
deltaU = deltaU1 + deltaU2## [kJ]
deltaH = deltaH1 + deltaH2## [kJ]
Q = Q1 + Q2## [kJ]
print "Change in Internal Energy is %.2f kJ\n"%(deltaU)#
print "Change in Enthalpy is %.2f kJ\n"%(deltaH)#
print "Heat Requirement is %.2f kJ\n"%(Q)#
from __future__ import division
from math import pi
print "Example: 2.17 - Page: 64\n\n"
# Solution
#*****Data*****#
D1 = 1## [m]
P1 = 120## [kPa]
P2 = 360## [kPa]
# P = k*D**3
#***************#
k = P1/D1**3## [proportionality constant]
D2 = (P2/k)**(1/3)## [m]
# Work done by the gas inside the balloon can be estimated as:
# W = integral(P*dV)#
# W = integral((k*D**3)*d((4/3)*pi*r**3)#
# W = (pi*k/6)*integral((D**3)*d(D**3))#
# W = (pi*k/12)*(D2**6 - D1**6)#
W = (pi*k/12)*(D2**6 - D1**6)## [kJ]
print "Workdone by the gas is %.2f kJ\n"%(W)#
from __future__ import division
print "Example: 2.18 - Page: 65\n\n"
# Solution
#*****Data*****#
P1 = 10*100## [kPa]
T1 = 250## [K]
P2 = 1*100## [kPa]
T2 = 300## [K]
R = 8.314## [J/mol K]
Cv = 20.78## [kJ/kmol K]
Cp = 29.10## [kJ/kmol K]
#**********#
V1 = R*T1/P1## [cubic m]
V2 = R*T2/P2## [cubic m]
# Calculation based on First Process:
# In this constant-volume process, the initial pressure of 10 bar is reduced to a final pressure of 1 bar and consequently the temperature decreases.
T_prime = P2*V1/R## [K]
deltaU1 = Cv*(T_prime - T1)## [kJ]
deltaH1 = deltaU1 + V1*(P2 -P1)## [kJ]
# Since V = constant
W1 = 0##[kJ]
# By first law of thermodynamics:
Q = W1 + deltaU1## [kJ]
# Calculation based on second process:
# In this process, the gas is heated at constant pressure to the final temperature of T2.
deltaH2 = Cp*(T2 - T_prime)## [kJ]
deltaU2 = deltaH2 - P2*(V2 - V1)## [kJ]
Q = deltaH2## [kJ]
W2 = Q - deltaU2## [kJ]
deltaU = deltaU1 + deltaU2## [kJ]
deltaH = deltaH1 + deltaH2## [kJ]
print "Change in Inernal Enrgy is %.2f kJ\n"%(deltaU)#
print "Change in Enthalpy is %.2f kJ\n"%(deltaH)#
from __future__ import division
print "Example: 2.19 - Page: 69\n\n"
# Solution
#*****Data*****#
T1 = 273## [K]
T2 = 273 + 67## [K]
m_dot = 20000## [kg/h]
Ws = -1.5## [hp]
Q = -38000## [kJ/min]
Z = 20## [m]
Cp = 4.2## [kJ/kg K]
g = 9.81## [m/second square]
#***************#
Q = Q*60/m_dot## [kJ/kg]
Ws = Ws*0.7457*3600/m_dot## [kJ/kg]
PE = g*Z*10**(-3)## [kJ/kg]
# KE is assumed to be negligible.
# For Steady Flow process: dE/dt = 0
# From Eqn. 2.47:
deltaH = Q - Ws - PE## [kJ/kg]
H1 = Cp*(T2 - T1)## [kJ/kg]
H2 = H1 + deltaH## [kJ/kg]
# Now, the temperature of the tank can be determined as:
T = (H2/Cp) + T1## [K]
print "Tempertaure of water in the second tank is %.2f K\n"%(T)#