Question

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

• A. 0.8141

Answer 1

The correct option is A 0.8141
Given:
$r_p=6$
$\gamma =1.4$
$\frac{T_{min}}{T_{max}}=0.3$ [for regenerative cycle]
${\eta }_{regenerativecycle}=1-\frac{T_{min}}{T_{max}}\times (r_p{)}^{\gamma -1/\gamma }$
$=1-0.3\times (6{)}^{\frac{0.4}{1.4}}$
$=0.49945$
${\eta }_{simplecycle}=1-\frac{1}{(r_p{)}^{\gamma -1/\gamma }}=1-\frac{1}{\left(6\right)\frac{1.4-1}{1.4}}$
$=0.4066$
Required ratio $=\frac{{\eta }_{simplecycle}}{{\eta }_{regenerativecycle}}=\frac{0.40666}{0.49945}$
$=0.8141$