$(3)40$ Points. Write a function that returns the lower heating value $($LHV$),$ on a mass basis, of

"any" mixture defined by Cantera GRI$30$ ideal gas object. For modeling the combustion process,

use "equilibrate" function at constant T$,$ P$.$ Use $25^($@$)$C$,1$atm as reference state and assume the

heating value is determined at constant T$\_("$ref$,")$P$\_($ref$).$ Name your function LHV$\_(\_)$mass$.$

Use your function to generate a table of lower heating values for the species listed below. $($You

can check your answer with the LHV table in your textbook!$)$

Hydrogen T $=25\%$

Methane T $=25$

Propane T $=25$

Carbon Dioxide T $=25$

Engineering Air T $=25$

For this problem, you should submit two m $-$files, i$.$e$.$ the LHV $\_$mass function and the main code

to generate the table above.

$(4)50$ Points. $($Brayton Cycle$)$ Construct a model of a simple$-$cycle gas turbine $($compressor$,$

burner, turbine$)$ using the natural gas mixture specified below with dry engineering air $($both at

$25^($@$)$C$,1$atm $)$:

Use a compressor pressure ratio of $20$:$1.$ Assume isentropic efficiencies for the compressor and

turbine of $90\%$ and $88\%,$ respectively. Inject the fuel into the combustor through nozzles that

have an inlet pressure that is twice the combustor air pressure. For this purpose, consider a fuel

compressor with the isentropic efficiency of $90\%.$ Assume adiabatic mixing between the air and

the fuel at the pressure of air, before combustion. Neglect pressure losses except for across the

combustor$-$use a $5\%$ loss of stagnation pressure there. Assume an allowable turbine inlet

temperature of $1600$ K $.$ Note that you will have to solve iteratively to find the correct fuel$-$to$-$air

flow ratio to generate this temperature. For modeling the combustion process, use "equilibrate"

function at constant H$,$ P$.$

Depict the cycle on a T$-$s diagram. Because the mass flow rates and compositions vary with

position in the cycle $($air$,$ fuel, air$-$fuel mixture, and products$),$ make the s coordinate of the T$-$s

diagram the entropy of the working fluid per unit mass of fuel. Calculate the LHV of the fuel

by using LHV$\_(\_)$mass function that you developed in $(3),$ the thermal efficiency of the cycle $($net

work $/$ fuel heating value provided$),$ and the air$-$specific work $($work per unit air flow in kg $).$

for your information, these are the Matlab problem using cantera. Please write codes