# Example 13.1     
 T1   =   -60.00 degC
 T2   =   -40.00 degC
 hig  =   2838.900 kJ/kg
 R   =   0.4615 kJ/kg degK
 Y = hig * (T2 - T1) / R / T1 / T2 
 P2   =   0.01290 kPa
 P1 = P2 / exp(Y) ; kPa 




# Example 13.1E     
 T1   =   -70.00 degF
 T2   =   -40.00 degF
 hig  =   948148.600 Btu/lbm
 R   =   85.7600 Btu/lbm/degF
 Y = hig * (T2 - T1) / R / T1 / T2     
 P2   =   0.0019000 psi
 P1 = P2 / exp(Y)  ; psi 

# Example 13.3     
 P1   =   0.10 Mpa
 P2   =   0.20 Mpa
 T0   =   25.00 degC
 R   =   0.2870 kJ/kg degK
 C0  =   1.0000 m^3 degK^3 / kg
 dels = -R * ln(P2 / P1) - 3 * C0 * (P2 - P1) / T0^4  ; kJ/kg/degK 

# Example 13.4     
 m0  =   1.00 kg
 P1   =   0.10 Mpa
 P2   =   100.00 Mpa
 T0   =   15.00 degC
 n  =   0.000114 m^3 / kg
 b  =   8.600E-12 m^2 / N
 a  =   5.000E-05  / degK
 w0 = -n * b * (P2^2 - P1^2) / 2  ; J/kg 
 dels = -n * a * (P2 - P1) ; J/kg / degK 
 q = T0 * dels  ; J/kg 
 delu = q - w0 ; J/kg 


# Example 13.5     
 P1   =   20.00 Mpa
 P2   =   2.00 Mpa
 T1    =   -70.00 degC
 fp   =   3.39 
 fT   =   126.20 
 Pr1 = P1 / fp  ; Mpa 
 Tr1  = T1 / fT  ; degC 
 Pr2 = P2 / fp  ; Mpa 
 R   =   0.2968 kJ/kg degK
 f  =   2.1000 
 Tc    =   126.20 degK
 delh1 = f * R * Tc  ; kJ/kg 
 Cp   =   1.0416 kJ/kg/degC
 T20    =   146.00 degK
 delh1h2 = Cp * (T1 - T20)   ; kJ/kg
 Tr2  = T20 / fT  ; degC 
 f  =   0.5000 
 delh2 = f * R * T20  ; kJ/kg 


## Example 13.6    
# P1 = 86.19 bar
# T1 = 310.94 degK
# P2   =   0.50 Mpa
# T2    =   125.00 degK
# fp   =   3.39 
# fT   =   126.20 
# Pr1 = P1 / fp  ; Mpa 
# Tr1  = T1 / fT  ; degK 
# Pr2 = P2 / fp  ; Mpa 
# Tr2  = T2 / fT  ; degK 
# R   =   0.2968 kJ/kg degK
# f1   =   2.5000 
# Tc    =   126.20 degK
# h10_minus_h1 = f1 * R * Tc  ; kJ/kg 
# f2   =   0.1500 
# h20_minus_h2 = f2 * R * Tc  ; kJ/kg 
# Cp   =   1.0416 kJ/kg/degC
# h10_minus_h20 = Cp * (T2 - T1)   ; kJ/kg 
# q = -(h20_minus_h2) - (h10_minus_h20) + (h10_minus_h1)  ; kJ/kg 
# c1   =   1.6000 
# s0p1T1_minus_Sp1T1 = c1 * R ; kJ/kg degK 
# c2   =   0.1000 
# s0p2T2_minus_Sp2T2 = c2 * R ; kJ/kg degK 
# s0p2T2_minus_S0p1T1 = Cp * ln(T2 / T1) - R * ln(P2 / P1)  ; kJ/kg degK 
# s2_minus_s1 = -(s0p2T2_minus_Sp2T2)+(s0p2T2_minus_S0p1T1) \
#   + (s0p1T1_minus_Sp1T1) ; kJ/kg 
# s2_minus_s1 * 1 degK; kJ / kg


## Example 13.7     
# fA   =   0.80 
# fCO2 = fA
# fB   =   0.20 
# fCH4 = fB
# P1   =   86.19 bar
# T1    =   310.94 degK
# n  =   0.00676 m^3/kg
# TCA   =   304.10 degK
# PCA   =   7.38 Mpa
# RA   =   0.1889 kJ/kg degK
# MA   =   44.0100 
# TCB   =   190.40 degK
# PCB   =   4.60 Mpa
# RB   =   0.5183 kJ/kg degK
# MB   =   16.0430 
# Rm = fCO2 * RA + fCH4 * RB  ; kJ/kg degK 
# yA = (fCO2 / MA) / (fCO2 / MA + fCH4 / MB)  
# yB = 1 - yA   
# TCM = yA * TCA + yB * TCB  ; degK 
# PCM = yA * PCA + yB * PCB  ; Mpa 
# Trm = T1 / TCM  
# Prm = P1 / PCM  
# Zm   =   0.7000 
# n0 = Zm * Rm * T1 / P1  ; m^3/kg 
# e = (n - n0) / n  
# aA = 27 * RA^2 * TCA^2 / 64 / PCA 
# bA = RA * TCA / 8 / PCA  ; m^3/kg 
# aB = 27 * RB^2 * TCB^2 / 64 / PCB 
# bB = RB * TCB / 8 / PCB  ; m^3/kg 
# am = (fA * aA^(1/2) + fB * aB^(1/2))^2  
# bm = fA * bA + fB * bB  ; m^3/kg 
# ng   =   0.006324 
# P2 = (Rm * T1 / (ng - bm) - am / ng^2 )

# Homework Problems:

TBD