In an ideal Brayton cycle with regeneration air is compressed from 1 bar and 300 K to 4 bar and 450 K, is heated to 750 K in the regenerator,and then further heated to 1200 K before entering the turbine. Under cold-air standard conditions. What is the effectiveness of the regenerator? [Take $γ = 1.3$ for gas]

71.18 %

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68.12 %

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65.14 %

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75.25 %

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Solution

The correct option is A 71.18 %

Given , $p_{1} = 1 b a r = p_{4}$

$p_{2} = 4 b a r = p_{3}$

$T_{1} = 300 K$

$T_{2} = 450 K$

$T_{a} = 750 K$

$T_{3} = 1200 K$

$\frac{T_{3}}{T_{4}} = {(\frac{p_{3}}{p_{4}})}^{\frac{γ - 1}{γ}}$

$\Rightarrow \frac{1200}{T_{4}} = {(\frac{4}{1})}^{\frac{0.3}{1.3}}$

$\Rightarrow T_{4} = 871.45 K$

$ε = \frac{T_{a} - T_{2}}{T_{4} - T_{2}} = \frac{750 - 450}{871.45 - 450} = 71.18 %$

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The correct option is A 71.18 % Given , p1=1 bar=p4 p2=4 bar=p3 T1=300 K T2=450 K Ta=750 K T3=1200 K T3T4=(p3p4)γ−1γ ⇒1200T4=(41)0.31.3 ⇒T4=871.45 K ε=Ta−T2T4−T2=750−450871.45−450=71.18%