Question

1. A Brayton cycle operates in air with a pressure ratio of 10. All components are ideal. The temperature at the inlet to the compressor is 400 K and the temperature at the inlet to the turbine is 2000 K. The kinetic energy at the inlet and exit of all components can be neglected. Assume that the working fluid has a constant cp=1000 J/kgK, and a specific ration of gamma=4.
   1. What is the compression work per unit mass?
   2. What is the turbine work per unit mass?
   3. What is the net work of the cycle per unit mass?
   4. What is the heat input per unit mass?
   5. What is the heat rejected per unit mass?
   6. What is the overall efficiency of the cycle?

Answer 1

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Brayton cycle & Wr Wc Apoc To = 10p , cp= 1000 J1kg K, Ti-Yook, T3 = 2000 K. 1 kJ/kg k T: 1-4 (typo in question et () 953-40640 altz = 773.28 x] - (2) 5 ) Tu s ceremony s ttg = 1035.89 ] o comprension wook (WC)a Wc = cp ( T2-T) = |(773.98-400) We = 372.28 kJ/kg] - 6 Turbine work (WI) - WT = Cp (T3 - Tu) = 1 (1000 - 1035.89) WT= 964.11 kJ/kg © Net work (What) - Wnet = WT- Wc = Whet = 591.83 kJ/kg + @ Heat input (a), asa Cpl T3-TR) =) ( Povo - 772.99) Os - 1727.72 kJ/kg 7 © Heat rejected (93) -> QRCpl Tu-To) = |(1035.89-400) [OR = 635.89 kJ/kg © Overall efficiency (9.) Yo - Wnet - 591 83 170 = 48.217.) as 1227-72