A simple Brayton cycle has a pressure ratio of 5 and a maximum temperature of 900 K. Air enters the compressor at 100 kPa, 300 K. Based upon cold-air standard analysis assumptions, the back-work ratio of this cycle is?

A simple Brayton cycle has a pressure ratio of 5 and a maximum temperature of 900 K. Air enters the compressor at 100 kPa, 300 K. Based upon cold-air standard analysis assumptions, the back-work ratio of this cycle is? Correct Answer 0.53

Using the pressure ratio and isentropic process relations, T2 = T1rp(k – 1) / k = 475 K and T4 = T3rp(1 – k) / k = 568 K. Application of the first law to the compressor and turbine processes and substituting the results into the back-work ratio definition produces rb = (T2 -T1) / (T3 -T4) = 0.53.
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