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# Answer to Question #101261 in Electrical Engineering for Muhammad Umar Aslam

Question #101261
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
1
2020-01-15T07:10:09-0500

we can write

"\\frac{T_2}{T_1} =\\frac{\\frac {p_2}{p_1}\u00d7(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\u00d71.74=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\u00d7(T_3-T_2)-c_p\u00d7(T_4-T_1)=223.5"

gross work is equal to

"gross work= c_p\u00d7(T_3-T_4)=441"

work ratio=0.5

ideal cycle efficiency 43%

work ratio=0.5

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