$($Elliott $3\mathrm{.}2$a$)$ One mole of methane gas, with a temperature$-$independent heat

capacity of $Cp=44\frac{J}{m}ol-K.$ held within a piston$/$cylinder at an initial con$-$

dition of $600K$ and $5$MPa. It undergoes two independent processes. The

following reversible steps are executed:

$($a$)$ Step $1$: The gas is expanded isothermally to $0\mathrm{.}2$MPa, absorbing a quan$-$

tity of heat

$($b$)$ The gas is cooled at constant volume to $300K.$

$($c$)$ Step $3.$ The gas is compressed isothermally to the initial volume.

$($d$)$ Step $4$: The gas is heated to the initial state at constant volume requiring

heat transfer $Q_{H2}.$

Calculate $U,Q,$ and $W_{EC}$ for each step and for the cycle. Also calculate the

thermal efficiency, that is$,$ the ratio of total work to heat furnished

${}_{th}=\frac{-W_{{?}_{?}}(EC,\text{c}\text{y}\text{c}\text{l}\text{e})}{Q_{{?}_{?}}(H1)+Q_{{?}_{?}}(H2)}$

$($a$)$ Step $1$: The gas is expanded to $3\mathrm{.}92$MPa isothermally, absorbing a quan$-$

tity of heat, $Q_{H1}$

$($b$)$ Step $2$: The gas is expanded adiabatically to $0\mathrm{.}1$MPa

$($c$)$ Step $3$: The gas is compressed isothermally to $0\mathrm{.}128$MPa.

$($d$)$ Step $4$: The gas is compressed adiabatically to the initial state.

Calculate $U,Q,$ and $W_{EC}$ for each step and for the cycle. Also calculate the

thermal efficiency, that is$,$ the ratio of total work to heat furnished.

${}_{th}=\frac{-W_{{?}_{?}}(EC,\text{c}\text{y}\text{c}\text{l}\text{e})}{Q_{{?}_{?}}(H1)}$

Thank you for your help. Sorry for such a long question