Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycle, the pressure ratio is $6$ and the ratio of the specific heats of the working medium is $1.4$ . The ratio of minimum to maximum temperatures is $0.3$ (with temperature expressed in K) in the regenerative cycle. The ratio of the thermal efficiency of the simple cycle to that of the regenerative cycle is
0.8141

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Solution

The correct option is A 0.8141
Given:
$r_{p} = 6$
$γ = 1.4$
$\frac{T_{m i n}}{T_{m a x}} = 0.3$ [for regenerative cycle]
$η_{r e g e n e r a t i v e c y c l e} = 1 - \frac{T_{m i n}}{T_{m a x}} \times (r_{p})^{γ - 1 / γ}$
$= 1 - 0.3 \times (6)^{\frac{0.4}{1.4}}$
$= 0.49945$
$η_{s i m p l e c y c l e} = 1 - \frac{1}{(r_{p})^{γ - 1 / γ}} = 1 - \frac{1}{(6) \frac{1.4 - 1}{1.4}}$
$= 0.4066$
Required ratio $= \frac{η_{s i m p l e c y c l e}}{η_{r e g e n e r a t i v e c y c l e}} = \frac{0.40666}{0.49945}$
$= 0.8141$

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The correct option is A 0.8141Given: rp=6 γ=1.4 TminTmax=0.3 [for regenerative cycle] ηregenerativecycle=1−TminTmax×(rp)γ−1/γ =1−0.3×(6)0.41.4 =0.49945 ηsimplecycle=1−1(rp)γ−1/γ=1−1(6)1.4−11.4 =0.4066 Required ratio =ηsimplecycleηregenerativecycle=0.406660.49945 =0.8141