$\backslash$#$948.$ Simple Brayton Cycle Analysis

A gas$-$turbine power plant operates a simple Brayton cycle between pressure limits of $90$ and $1600$ kPa $.$ The working fluid is air, which enters the compressor at $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ at a rate of $\backslash (1000\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$min$\}\backslash ).$ The air is heated in a combustion chamber, entering the turbine at $\backslash (1200\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and leaving the turbine at $600.$ Assuming a compressor isentropic efficiency of $84$ percent and a turbine isentropic efficiency of $88$ percent, determine the following. Use specific constant heats with $\backslash ($ c$\_\{$v$\}=\mathrm{.}821\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kgK$\}\backslash ),\backslash ($ c$\_\{$p$\}=1\mathrm{.}108\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kgK$\}\backslash ),$ and $\backslash ($ k$=\backslash )1\mathrm{.}35.$

Note: this problem is actually overconstrained. With a sufficiently advanced equation solver, we could calculate the enthalpy after the combustion chamber without being given the temperature. Here a temperature is given for the sake of simplicity.

Find the net power output.

number $($rtol$=0\mathrm{.}05,$ atol$=1$e$-08)$

Find the back work ratio.

number $($rtol$=0\mathrm{.}05,$ atol$=1$e$-08)$

Find the thermal efficiency.

number $($rtol$=0\mathrm{.}05,$ atol$=1$e$-08)$