Plase explain every detail thoroughly. Consider a polytropic piston$-$cylinder device containing nitrogen gas at a specified state, where $V_1=0\mathrm{.}07m^3,T_1=180Cand{P}_1=130$kPa are the initial variables. The properties of nitrogen are $R=0\mathrm{.}2968k\frac{J}{k}g*K$ and $k=1\mathrm{.}395.$

$3\mathrm{.}1$ The mass of nitrogen gas is

a$.m=0\mathrm{.}06768Kg$

b$.m=0\mathrm{.}67680Kg$

c$.m=0\mathrm{.}09136Kg$

d$.$ None of the above

$3\mathrm{.}2$ The volume of nitrogen at the final state $2$ is

a$.V_2=0\mathrm{.}09914m^3$

b$.V_2=0\mathrm{.}99140m^3$

c$.V_2=0\mathrm{.}03723m^3$

d$.$ None of the above

$3\mathrm{.}3$ The Final temperature is

a$.T_2=395K$

b$.T_2=39\mathrm{.}50K$

c$.T_2=912K$

d$.$ None of the above

$3\mathrm{.}4$ The boundary work is

a$.W_b=2\mathrm{.}96kJ$

b$.W_b=29\mathrm{.}60kJ$

c$.W_b=8\mathrm{.}23kJ$

d$.$ None of the above

$3\mathrm{.}5$ The positive sign indicates that the work is done by the system $($work output$).$

True False