Question

A closed cycle gas turbine unit operating is maximum and minimum temperature of 760 and 20 degree Celsius has a pressure ratio of 7/1. Calculate the ideal cycle efficiency and the work ratio

Answer 1

we can write

$\frac{T_2}{T_1} =\frac{\frac {p_2}{p_1}×(r-1)} {r} (1)$

Where $\frac {p_2}{p_1}=7$ , r=1.4

Using (1) we get

$\frac{T_2}{T_1} =1.74$

In our case, we have T₁=293 K

$T_2=T_1×1.74=509.8 K$

$\frac{T_2}{T_1} =\frac{T_3}{T_4} (2)$

In our case, we have T₃=1033 K

$T_4=\frac{1033}{1.74} =593.7 K$

the ideal cycle efficiency is equal to

$k=1-\frac{T_4-T_1}{T_3-T_2} =43$

work ratio is equal to

$work ratio=\frac{net work}{gross work} (3)$

net work is equal to

$net work=c_p×(T_3-T_2)-c_p×(T_4-T_1)=223.5$

gross work is equal to

$gross work= c_p×(T_3-T_4)=441$

work ratio=0.5

Answer

ideal cycle efficiency 43%

work ratio=0.5