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HW7_Solution

# HW7_Solution - Problem5.20 Known: coldreservoirs...

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Problem 5.20 Known: Data are provided for four cases involving reversible power cycles operating between hot and cold reservoirs. Schematic & Given Data: Fig. P.5.20 Symbols: : efficiency : net amount of energy transfer by work : amount of energy transfer by heat at hot reservoir : amount of energy transfer by heat at cold reservoir cycle H L W Q Q η Analysis: Thermal efficiency of a system undergoing a reversible power cycle is max 1 C H T T η = (Eq.5.9) (a) 1200K, =300K. Find H C T T η = With Eq.5.9, 300K 1 1 0.75 (75%) 1200K C H T T η = = = (b) 500 C, =20 C, =1000kJ. Find and H C cycle C H T T W Q Q = ° ° With Eq.5.9 and cycle H W Q η = , which applies for any power cycle, 1000kJ 1 1610kJ 293K 1 1 773K cycle cycle C H C H H H W W T Q T Q T T = = = = For any power cycle, cycle H C W Q Q = ; thus, 1610kJ 1000kJ=610kJ C H cycle Q Q W = =

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(c) 60%, =40 F. Find C H T T η = ° With Eq.5.9, 500 R 1 0.60 1 1250 R (790 F) C H H H T T T T η ° = = = ° ° (d) 40%, =727 C. Find H C T T η = ° With Eq.5.9, 1 0.40 1 600K (327 C) 1000K C C C H T T T T η = = = °
Problem 5.38 Known: Steady state operating data are provided for a power plant discharging energy by heat transfer to a river. Find: Determine the increase in the temperature of the river traceable to such heat transfer for each of two cases. Schematic & Given Data: Model and Assumptions: 1. The power plant is modeled as a power cycle operating at steady state. 2. The combustion products provide energy by heat transfer to the power cycle. Energy is discharged by heat transfer to the river. These are the only heat transfers. 3. The river water is modeled as incompressible with constant specific heat C. Symbols: : efficiency : net rate of work : recieved heat transfer rate : discharged heat transfer rate cycle in out W Q Q η ± ± ± Analysis: For a control volume enclosing a section of the river, as shown in the sketch an energy rate balance reduces to give [ ] 2 1 out Q m h h = ± ± where out Q ± is a positive number denoting the energy discharged from the power cycle to the river. With

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