PLEASE ELABORATE HOW TO DO THIS EQUATION, please WRITE THE NUMBER OF EACH PARAMETER BECAUSE I DONT KNOW WHAT NUMBER I SHOULD PUT ANSWER THIS QUESTION BProblem $4.$ A gas turbine power plant operating on the Brayton cycle has a pressure ratio of $8.$ The isentropic efficiency of the compressor and expander is $85\%$ and $75\%,$ respectively. The nominal power produced is $4500$ kW $.$ Air is used at $1$ bar and $30C,$ the exhaust gas temperature leaving the turbine is $550C$ and is considered an ideal gas $)=(29\frac{J}{\text{m}\text{o}\text{l}\text{K}}.$ If the following assumptions are used:

Air and flue gas behave like ideal gases

$,$ Air molecular weight composition $=79\%N_2$ and $21\%O_2)$

$=\frac{Cp}{Cv}=1\mathrm{.}4$

Tim Divisi Akademik HIMATEK$-$ITB $2023/2024$

$39$

TK$3102-$ Sistem Utilitas

Temperature conversion, $K=C+273,15$

Molecular weight of natural gas $=$ air $=28,84k\frac{g}{k}$mol

a$.$ Determine the air flow rate entering the compressor.

Hint:

The Brayton Cycle has the following illustration

The pressure ratio can be related to the output and input temperatures with the following equation $)>(P_1$

$\frac{T_{\text{o}\text{u}\text{t}}^{IS}}{T_{in}}=(\frac{P_2}{P_1}{)}^{\frac{-1}{}}$

By obtaining $T_{\text{o}\text{u}\text{t}}$ isentropic$,T_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}$ can be obtained with the efficiency calculations for the compressor and expander as follows.

${}_{\text{k}\text{o}\text{m}\text{p}}=\frac{T_{\text{o}\text{u}\text{t}}^{IS}-T_{in}}{T_{\text{o}\text{u}\text{t}}-T_{in}},{}_{\text{e}\text{k}\text{s}}=\frac{T_{in}-T_{\text{o}\text{u}\text{t}}}{T_{in}-T_{\text{o}\text{u}\text{t}}}$

The total power produced by the gas turbine can be calculated using the following equation

$W_{\text{t}\text{o}\text{t}\text{a}\text{l}}=n_{\text{u}\text{d}\text{a}\text{r}\text{a}}^{}C{p}_{\text{u}\text{d}\text{a}\text{r}\text{a}}(T_{\text{e}\text{k}\text{s}}-T_{\text{c}\text{o}\text{m}\text{p}})$

Answer: ${?}_{(})$ Air flow rate entering the compressor $=1,33$kmo$\frac{l}{s}=138085\mathrm{.}92k\frac{g}{h}$our.

b$.$ Determine the need for natural gas fuel if the calorific value is $800M\frac{J}{k}$mol.

Hint: