ब्रेटन चक्र में, हवा 300 K पर संपीडक में प्रवेश करती है और चक्र का अधिकतम तापमान 1200 K है। अधिकतम शक्ति उत्पादन के लिए चक्र की तापीय दक्षता कितनी होगी?

Concept:

A gas turbine work on Brayton cycle, Thermal Efficiency of Brayton cycle is given by 

 \({\eta _{th}} = 1 - \frac{1}{{{{\left( {{r_p}} \right)}^{\frac{{\gamma - 1}}{\gamma }}}}}\)where rp = pressure ratio, \(r_p=\frac{P_2}{P_1}\)

For Maximum work : \({r_p} = {\left( {\frac{{{T_3}}}{{{T_1}}}} \right)^{\frac{\gamma }{{2\left( {\gamma - 1} \right)}}}}\)

Where T3 is the maximum temperature in the cycle which is at the inlet of the turbine,

and T1 is the minimum temperature in the cycle which is at the inlet of the compressor now if we put the maximum compression ratio in the thermal efficiency formula then 

\({\eta _{th}} = 1 - \sqrt {\frac{{{T_1}}}{{{T_3}}}} = 1 - \sqrt {\frac{{{T_{min}}}}{{{T_{max}}}}} \)

Calculation:

Given, temperature limits, T3 = 1200 K, and T1 = 300 K

So \({\eta _{th}} = 1 - \sqrt {\frac{{{T_1}}}{{{T_3}}}} = 1 - \sqrt {\frac{{{T_{min}}}}{{{T_{max}}}}} \)

\({\eta _{th}} = 1 - \sqrt {\frac{{300}}{{1200}}} = 0.5\;or\;50\% \)