# Chapter 8 : Production Of Power From Heat¶

## Example 8.1 page no : 121¶

In [2]:
# Variables
#(a)-As in Example(7.6)
P1 = 8600.;			#[KPa]
T1 = 773.15;			#[K]
#values of Enthalpy and Entropy from Steam tables
H1 = 3391.6;			#[KJ/Kg]
S1 = 6.6858;			#[KJ/Kg/K]

P2 = 10;			#[KPa]
S2i = S1;			#Isentropic

S2_liquid = 0.6493;
S2_vapor = 8.1511;
H2_liquid = 191.8;
H2_vapor = 2584.8;

# Calculations and Results
x2 = (S2i-S2_liquid)/(S2_vapor-S2_liquid);

H2i = H2_liquid+(x2*(H2_vapor-H2_liquid));
del_Hs_1 = round((H2i-H1),1);			#[KJ/Kg]
Ws = del_Hs_1;
H3i = H2i;
H4 = H2_liquid;
#Applying Eqn(8.2)
Q_condenser = round((H4-H3i),1);			#heat Of condenser  [KJ/Kg]
#From Example(7.10)
#Properties of saturated liquid water @ 318.15K
V = 1010;			#[cm**3/Kg]
V = 1010*10**-6;			#[m**3/Kg]
Beta = 425*10**-6;			#[K**-1]
Cp = 4.178;			#[KJ/Kg/K]

#From Eqn(7.24)
Ws_2 = round((V*(P1-P2)),1)			#[KPa m**3/Kg]
del_Hs_2 = Ws_2;
H1 = H4+del_Hs_2;
#Enthalpy Of saturated steam at 8600KPa and 773.15K
H2 = 3391.6;			#[KJ/Kg]
#Applying Eqn(8.2)
Q_boiler = H2-H1;

Ws_Rankine = -Q_boiler-Q_condenser;
eta = round((abs(Ws_Rankine)/Q_boiler),3);
print ('(a)Rankine Cycle')
print 'Thermal Efficiency',eta

#(b)
eta_b = 0.75;
del_H_1 = del_Hs_1*eta_b;
Ws_turbine = del_H_1;
H3 = H2+del_H_1;
Q_condenser = H4-H3;

#By Example 7.10 for the pump
Ws_pump = del_Hs_2/eta_b;
del_H_2 = Ws_pump;
Ws_net = Ws_turbine+Ws_pump;
H1 = H4+del_H_2;

Q_boiler = H2-H1;
efficiency = round(abs(Ws_net)/Q_boiler,4);
print ('(b)Practical cycle with 0.75 efficiency')
print 'Thermal Efficiency',efficiency

#(c)
#By rating of Power Cycle
rWs_net = -80000;			#[KJ/s]  Power Rating
rm = round(rWs_net/Ws_net,2);

rQ_boiler = round(rm*Q_boiler/1000,1);			#[MW]
rQ_condenser = round(rm*Q_condenser/1000,1);			#[MW]
print ('(c)By rating of Power Cycle');
print 'Steam Rate',rm,'kg/s'
print 'Heat Transfer rate in boiler',rQ_boiler,'MW'
print 'Heat Transfer rate in condenser',rQ_condenser,'MW'

(a)Rankine Cycle
Thermal Efficiency 0.397
(b)Practical cycle with 0.75 efficiency
Thermal Efficiency 0.2961
(c)By rating of Power Cycle
Steam Rate 84.74 kg/s
Heat Transfer rate in boiler 270.2 MW
Heat Transfer rate in condenser -190.2 MW


## Example 8.4 page no : 122¶

In [3]:
# Variables
K = 6.;			#Pb/Pa
T1 = 298.15;			#[K]
Tmax = 1033.15;			#[K]
Gamma = 1.4;

# Calculations and Results
#(a)  Gamma = 1.4
#From Eqn(8.12)
eta_a = round(1-((1/K)**((Gamma-1)/Gamma)),1);
print ('(a)Efficiency of an ideal air cycle')
print 'Efficiency',eta_a

#(b)  eta_c = 0.83  eta_t = 0.86
eta_c = 0.83;
eta_t = 0.86;
K2 = Tmax/T1;
alpha = (K)**((Gamma-1)/Gamma);

#Umath.sing Eqn(8.13)
eta_b = round(((eta_t*eta_c*K2*(1-(1/alpha)))-(alpha-1))/((eta_c*(K2-1))-(alpha-1)),3);
print ('(b)Thermal efficiency of an air cycle if the Compressor and Turbine Operate adiabatically')
print 'Thermal efficiency',eta_b

(a)Efficiency of an ideal air cycle
Efficiency 0.4
(b)Thermal efficiency of an air cycle if the Compressor and Turbine Operate adiabatically
Thermal efficiency 0.234