GATE 2024 ME – Question 45

Thermal Engineering Applications · Power Engineering: vapour and gas power cycles, regeneration and reheat · 2 marks · Numerical answer

Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at 100 kPa and 300 K and exits the compressor at 600 kPa and 550 K. The air exits the combustion chamber at 1250 K and exits the adiabatic turbine at 100 kPa and 800 K. The exhaust air from the turbine is used to preheat the air in the regenerator. The exhaust air exits the regenerator (state 6) at 600 K. There is no pressure drop across the regenerator and the combustion chamber. Also, there is no heat loss from the regenerator to the surroundings. The ratio of specific heats at constant pressure and volume is $c_p/c_v = 1.4$. The thermal efficiency of the cycle is _________ % (*answer in integer*).

A Brayton cycle with a compressor (state 1 to 2), a regenerator (2 to 3 on the cold side), a combustion chamber (3 to 4), a turbine (4 to 5) and the hot exhaust passing back through the regenerator (5 to 6).

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Correct answer: 40

Explanation

Energy balance on the regenerator, with the same $c_p$ on both sides: $T_3 - T_2 = T_5 - T_6 = 800 - 600 = 200$ K, so $T_3 = 550 + 200 = 750$ K. The heat added is $c_p(T_4 - T_3) = c_p(1250 - 750) = 500c_p$. The net work is $c_p\left[(T_4 - T_5) - (T_2 - T_1)\right] = c_p\left[(1250 - 800) - (550 - 300)\right] = 200c_p$. So $\eta = \frac{200}{500} = 0.40$, which is 40 %.