Air enters a compressor at 100 kPa and $30^{\circ} C$ in a Brayton cycle. The air pressure after compression is 500 kPa. If the heat added is 623 kJ/kg, the back work ratio for the cycle is____.
(For air, $γ = 1.4 a n d C_{p} = 1.005 k J / k g K$ )
0.436

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Solution

The correct option is A 0.436

$T_{1} = 303 K; γ = 1.4$
$T_{2} = T_{1} (r_{p}) \frac{γ - 1}{γ}$
$∴ r_{p} = \frac{500}{100} = 5$
So, $T_{2} = 3030 (5)^{\frac{1.4 - 1}{1.4}}$
$T_{2} = 479.897 K$
Now, $H A = C_{p} (T_{3} - T_{2})$
$623 = 1.005 (T_{3} - 479.897)$
$T_{S} = 1099.797 K$
So, $T_{4} = \frac{T_{3}}{(γ_{p})^{\frac{γ - 1}{γ}}} = \frac{1099.797}{(5)^{\frac{1.4 - 1}{1.4}}}$
$T_{4} = 494.39 K$
Back work ratio, $r_{b w} = \frac{W_{C}}{W_{T}} = \frac{T_{2} - T_{1}}{T_{3} - T_{4}}$
$r_{b w} = \frac{479.8597 - 303}{1099.797 - 694.39} = 0.436$

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Air enters a compressor at 100 kPa and 30∘C in a Brayton cycle. The air pressure after compression is 500 kPa. If the heat added is 623 kJ/kg, the back work ratio for the cycle is____. (For air, γ=1.4andCp=1.005kJ/kgK)0.436

Air enters a compressor at 100 kPa and $30^{\circ} C$ in a Brayton cycle. The air pressure after compression is 500 kPa. If the heat added is 623 kJ/kg, the back work ratio for the cycle is____.
(For air, $γ = 1.4 a n d C_{p} = 1.005 k J / k g K$ )
0.436