In this problem, methane enters a reaction chamber at $0\mathrm{.}5$atm and $298K$ under

steady$-$state, steady$-$flow conditions. The products exit the reaction chamber as solid

carbon, $C(s),$ and a gas mixture of $C{H}_4$ and $H_2$ at a temperature of $1500K.$ The gas

products exit at the same pressure as the inlet $(0\mathrm{.}5$atm$).$ The mole fraction of

hydrogen in the product gas mixture $($i$.$e$.,$ not including the solid carbon$)$ is measured

to be $y_{H2}=0\mathrm{.}6.$ In the following questions, calculations of gravimetric specific

enthalpy $($in $k\frac{J}{k}g)$ of a particular species should be derived from the molar enthalpy

of formation and deviation from the standard state, which is

atm$).$ The solid carbon can be assumed to have a constant specific heat of $c_p=1\mathrm{.}0$

$k\frac{J}{kgK}$ over the temperature range of interest.

$($Use the formal problem$-$solving template with the Known, Schematic &

Given Data, and Find sections, and place your final answers in the boxes next

to the corresponding part of the question$).$

a$)$ Complete the following table of gravimetric specific enthalpies $($in $k\frac{J}{k}g).$

b$)$ If the inlet methane mass flow rate is $0\mathrm{.}001k\frac{g}{sec},$ calculate the rate of net

heat addition $($in $kW),$ neglecting any kinetic and potential energy effects.

c$)$ Complete the following table of gravimetric specific flow exergy values $($in

$k\frac{J}{k}g),$ neglecting any kinetic and potential energy effects.