Project ForgeFor the same Brayton cycle described above (pressure ratio 8, compressor inlet 300 K, turbine inlet 1400 K, both isentropic efficiencies 0.8, cp=1 kJ/kgK, γ=1.4, compressor power 304.3 kJ/kg from the actual compressor work), the thermal efficiency of the cycle in percentage (%) is
- 24.8
- B38.6
- C44.8
- D53.1
Explanation
Ideal turbine exit: T4s=T3/rp^((γ−1)/γ)=1400/1.8114=772.9K. Ideal turbine work=cp(T3−T4s)=627.1 kJ/kg; actual Wt=ηt×627.1=0.8×627.1=501.7 kJ/kg. Net work=Wt−Wc=501.7−304.3=197.4 kJ/kg. Actual compressor-exit temperature (from actual work): T2=T1+Wc/cp=300+304.3=604.3K. Heat input Qin=cp(T3−T2)=1400−604.3=795.7 kJ/kg. Efficiency=Wnet/Qin=197.4/795.7≈0.248=24.8%.
Source: GATE ME 2013 (Booklet Code A) (2013)
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