# Chapter 14 : Real Gases Compressiblity¶

### Example 14.1 Page No. 442¶

In [4]:
# Variables
T1f = 125. ;			# Temperature of NH3 -[degree F]
T1 =  460. +T1f ;			# Temperature NH3 -[degree Rankine]
Pg =  292. ;			# Pressure of NH3 -[psig]
Pa =  Pg+14.7 ;			#Pressure of NH3 -[psia]
R = 10.73 ;			#Universal gas constant-[(psia*cubic feet)/(lb mol*R)]
mw_NH3 = 17. ;		# Molecular wt. 1 lb mol NH3-[lb]
n = 1/17. ;			#[mol]
V_tank = 120. ;		# Volume of tank-[cubic feet]

# Calculations
V_id = (n*R*T1)/Pa ;	# Specific volume of NH3 treating it ideal gas-[cubic feet/lb]
Tc = 729.9 ;			#[degree R]
Pc = 1636. ;			#[psia]
Tr =  T1/Tc;
Pr =  Pa/Pc;

z_real = 0.855;
z_ideal = 1.;
V_real =  V_id*z_real/z_ideal;			# Specific volume of NH3 treating it real gas-[cubic feet/lb]
NH3 = V_tank/V_real ;			        # Actual amt. of NH3 in tank-[lb]

# Results
print 'Actual amt. of NH3 in tank is %.0f lb. Therefore , boss is wrong.'%NH3

Actual amt. of NH3 in tank is 117 lb. Therefore , boss is wrong.


### Example 14.2 Page No. 444¶

In [5]:
# Variables
Tc = 154.4 ;			#[K]
Pc1 = 49.7 ;			# [atm]
Pc = 101.3 * Pc1;		#[kPa]

T_O21 = -25 ;			# Temperature-[degree C]
T_O2 =  273+T_O21;		#Temperature -[K]
R = 8.134 ;			    # gas constant-[(cubic metre * kPa)/(kg mol * K)]
V_tank = 0.0284 ;		# Volume of tank-[cubic metre]
mol_O2 = 32 ;			# Kmol. wt. of O2-[kg]
m_O2 =  3.5 ;			# Mass of liquid O2-[kg]

# Calculations
V_sp = V_tank * mol_O2/m_O2 ;			# Specific molar volume-[m**3/kg]
Vc = R * Tc/Pc ;			            # [cubic metre/kg mol]
Vr = V_sp/Vc;
Tr = T_O2/Tc;

Pr = 1.43 ;			# [kPa]
P_O2 = Pr * Pc ;	# The pressure in the tank -[kPa]

# Results
print 'The pressure in the tank is %.2f  kPa.'%P_O2

The pressure in the tank is 7199.49  kPa.


### Example 14.3 Page No. 448¶

In [6]:
# Variables
Tc = 100. ;			# Temperature  -[degree C]
T   =  273 +Tc ;	# Temperature -[K]
P   =  90. ;		# Pressure [atm]
R = 82.06 ;			# gas constant-[(cubic centimetre * atm)/(g mol * K)]
Y_CH4  = 20./100 ;			# [mole fraction]
Y_C2H4 = 30./100 ;			# [mole fraction]
Y_N2   =  50./100 ;			#[mole fraction]

Tc_CH4 = 191. ;			#[K]
Pc_CH4 = 45.8 ;			# [atm]
Tc_C2H4 = 283. ;		#[K]
Pc_C2H4 = 50.5 ;		# [atm]
Tc_N2 = 126. ;			#[K]
Pc_N2 = 33.5 ;			# [atm]

# Calculations & Results
#(a)-Ideal gas law
V_sp1 = R * T/P ;			# Molar volume-[cubic centimetre/g mol]

print '(a) The volume per mole of mixture by ideal gas law is %.1f cubic centimetre/g mol.'%V_sp1

#(b)
Pc_mix = Pc_CH4 * Y_CH4+Pc_C2H4 * Y_C2H4+Pc_N2 * Y_N2;			# [atm]
Tc_mix = Tc_CH4 * Y_CH4+Tc_C2H4 * Y_C2H4+Tc_N2 * Y_N2 ;			# [K]
Pr_mix = P/Pc_mix;
Tr_mix = T/Tc_mix;
# With 2 parameters(Pr_mix and Tr_mix) , you can find from figure 14.4b that z * Tr_mix = 1.91
z = 1.91/Tr_mix;
V_sp2 = z * R * T/P ;			# Molar volume-[cubic centimetre/g mol]
print '(b) The volume per mole of mixture by treating it to be real gas is %.1f cubic centimetre/g mol.'%V_sp2

(a) The volume per mole of mixture by ideal gas law is 340.1 cubic centimetre/g mol.
(b) The volume per mole of mixture by treating it to be real gas is 324.1 cubic centimetre/g mol.

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