Explanation Show the T-s diagram as in Figure (1). Express temperature at state 6 s . T 6 s = T 5 [ P 6 P 5 ] k − 1 k (I) Here, temperature at state 5 is T 5 , pressure at state 6 is P 6 , pressure at state 5 is P 5 and heat capacity ratio is k . Express temperature at state 6 using Carnot efficiency. T 6 = T 5 + T 6 s − T 5 η C , i (II) Here, temperature at state 6 is T 6 , temperature at state 6 s is T 6 s and initial isentropic efficiency of turbine is η C , i . Express temperature at state 8 s . T 8 s = T 7 [ P 8 P 7 ] k − 1 k (III) Here, temperature at state 7 is T 7 , pressure at state 8 and 7 is P 8 and P 7 respectively. Express temperature at state 8. T 8 = T 7 − η C , i ( T 7 − T 8 s ) (IV) Here, temperature at state 7 is T 7 . Express temperature at state 9. T 9 = T sat@800 psia + 50 R (V) Here, saturation temperature at pressure of 800 psia is T sat@800 psia . Express enthalpy at state 1. h 1 = h f @ 5 psia (VI) Here, enthalpy of saturation liquid at pressure of 5 psia is h f @ 5 psia . Express specific volume at state 1. v 1 = v f @ 5 psia (VII) Here, specific volume of saturation liquid at pressure of 5 psia is v f @ 5 psia . Express work done at inlet. w p,in = v 1 ( P 2 − P 1 ) (VIII) Express enthalpy at state 2. h 2 = h 1 + w p,in (IX) Here, enthalpy at state 1 is h 1 . Due to throttling process, write the entropy at state 3 is equal to entropy at state 4. s 4 = s 3 (X) Here, entropy at state 3 is s 3 and entropy at state 4 is s 4 . Express enthalpy at state 4. h 4 = h 3 − η T ( h 3 − h 4 s ) (XI) Here, enthalpy at state 3 is h 3 and isentropic efficiency of turbine is η T . Express the net work output of gas cycle. w net,gas cycle = c p ( T 7 − T 8 ) − c p ( T 6 − T 5 ) = c p ( T 7 − T 8 − T 6 + T 5 ) (XII) Here, specific heat constant is c p , temperature at state 5, 6, 7 and 8 is T 5 , T 6 , T 7 and T 8 respectively. Express the net work output of steam cycle. w net,steam cycle = ( h 3 − h 4 ) − w p,in (XIII) Express mass flow rate of water from an energy balance. m ˙ w = c p ( T 8 − T 9 ) h 3 − h 2 m ˙ a (XIV) Here, mass flow rate of air is m ˙ a . Express heat input to the system. q in = c p ( T 7 − T 6 ) (XV) Express heat supplied from the system. q out = c p ( T 9 − T 5 ) + m ˙ w m ˙ a ( h 4 − h 1 ) (XVI) Express the overall thermal efficiency of the combined cycle. η th = 1 − q out q in (XVII) Conclusion: Refer Table A-2E, “ideal gas specific heats of various common gases”, and write the value of specific heat constant of air and heat capacity of air. c p = 0.240 Btu / lbm ⋅ R k = 1.4 Substitute 80°F for T 5 , 10 for P 6 P 5 and 1.4 for k in Equation (I). T 6 s = ( 80°F ) ( 10 ) 1.4 − 1 1.4 = [ ( 80 + 460 ) R ] ( 1.9306 ) = ( 540 R ) ( 1.9306 ) = 1043 R Substitute 80°F for T 5 , 1043 R for T 6 s and 0.90 for η C , i in Equation (II). T 6 = ( 80°F ) + 1043 R − 80°F 0.90 = ( 540 R ) + 1043 R − 540 R 0.90 = 1099 R Substitute 2100°F for T 7 , 1 10 for P 8 P 7 and 1.4 for k in Equation (III). T 8 s = ( 2100°F ) [ 1 10 ] 1.4 − 1 1.4 = [ ( 2100 + 460 ) R ] ( 0.5179 ) = ( 2560 R ) ( 0.5179 ) = 1326 R Substitute 2100°F for T 7 , 0.90 for η C , i and 1326 R for T 8 s in Equation (IV). T 8 = ( 2100°F ) − ( 0.90 ) ( 2100°F − 1326 R ) = ( 2560 R ) − ( 0.90 ) ( 2560 R − 1326 R ) = 1449 R Refer Table A-5E, “saturated water-pressure table”, and write the saturation temperature at pressure of 800 psia . T sat@800 psia = 518 °F Substitute 518 °F for T sat@800 psia in Equation (V). T 9 = 518 °F + 50 R = ( 518 + 460 ) R + 50 R = 978 R + 50 R = 1028 R Refer Table A-5E, “saturated water-pressure table”, and write the enthalpy of saturation liquid at pressure of 5 psia . h f @ 5 psia = 130.18 Btu / lbm Substitute 130.18 Btu / lbm for h f @ 5 psia in Equation (VI). h 1 = 130.18 Btu / lbm Refer Table A-5E, “saturated water-pressure table”, and write the specific volume of saturation liquid at pressure of 5 psia . v f @ 5 psia = 0.01641 ft 3 / lbm Substitute 0.01641 ft 3 / lbm for v f @ 5 psia in Equation (VII). v 1 = 0.01641 ft 3 / lbm Substitute 0.01641 ft 3 / lbm for v 1 , 800 psia for P 2 and 5 psia for P 1 in Equation (VIII). w p,in = ( 0.01641 ft 3 / lbm ) ( 800 psia − 5 psia ) = ( 0.01641 ft 3 / lbm ) ( 795 psia ) [ Btu 5.404 psia ⋅ ft 3 ] = 2

8th Edition

ISBN: 8220102809444

Author: CENGEL

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 10.9, Problem 101RP

To determine

The overall thermal efficiency of the combined cycle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.9, Problem 100RP

Chapter 10.9, Problem 102RP

Students have asked these similar questions

In a combined gas-steam power cycle the gas-turbine operates on a 10:1 pressure ratio with compressor and turbine-inlet temperatures of 300 K and 1345 K, respectively. The adiabatic efficiencies of the compressor and turbine are 86 and 89 percent respectively. The gas turbine exhaust, used as the energy source for a steam cycle, leaves the heat exchanger (steam boiler) at 470 K. The inlet conditions to the 85 percent efficient turbine in the steam cycle are 100 bars and 500 ºC. The condenser pressure is 0.10 bars, and the pump is 70 percent efficient. Using constant specific heat properties for air from Table A.5, determine (a) the heat input to the air, in kJ/kg of air, (b) the mass-flow rate ratio of air to steam, in kg-of air/kg of steam, (c) the net work of the gas-turbine cycle, in kJ/kg of air, (d) the net work of the steam cycle, in kJ/kg of steam, and (e) the overall thermal efficiency of the combined cycle.(1 bar = 100 KPa)

A steam Rankine cycle operates between the pressure limits of 1500 psia in the boiler and 2 psia in the condenser. The turbine inlet temperature is 800F. The turbine isentropic efficiency is 90 percent, the pump losses are negligible, and the cycle is sized to produce 2500 kW of power. Calculate the mass flow rate through the boiler, the power produced by the turbine, the rate of heat supply in the boiler, and the thermal efficiency.

A gas turbine unit consists of a compressor, heat exchanger, combustion chamber and turbine. The compressor and turbine are connected with a shaft. The unit operates between pressure limits of 100kPa and 625kPa. The cycle temperatures are: 28°C at compressor inlet, 625°C at the turbine inlet and 375°C at the turbine exhaust. The isentropic efficiency of the compressor is 85% and the effectiveness of the heat exchanger is 85%. If the net power is 1.5MW, calculate: (a). the temperature at compressor delivery (b). the isentropic efficiency of the turbine (c). the thermal efficiency of the cycle (d). the air-fuel ratio (e). the specific fuel consumption (f). the daily fuel consumption at the given power.

Chapter 10 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

Ch. 10.9 - Why is the Carnot cycle not a realistic model for...Ch. 10.9 - Prob. 2P Ch. 10.9 - A steady-flow Carnot cycle uses water as the...Ch. 10.9 - A steady-flow Carnot cycle uses water as the...Ch. 10.9 - Consider a steady-flow Carnot cycle with water as...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - How do actual vapor power cycles differ from...Ch. 10.9 - The entropy of steam increases in actual steam...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The overall thermal efficiency of the combined cycle.

Solution Summary: The author explains the overall thermal efficiency of the combined cycle.

Videos

The overall thermal efficiency of the combined cycle.

Want to see the full answer?

Chapter 10 Solutions