$($b$)$ Nitrogen $(N_2((g)))$ costs $$12\mathrm{.}74$ per $100$ standard cubic foot $($SCF$)($measured at $1$atm and $60F(15\mathrm{.}5C)).$ Liquid Nitrogen $(L{N}_2)$ costs $$14\mathrm{.}27$ per litre. The specific gravity of $L{N}_2$ is $0\mathrm{.}808.$ Compare the costs of $N_2(g)$ and $LN{N}_2$ on a $ per $kg$ basis.

Molecular weight of nitrogen $28$

Universal Gas Constant, $R=8\mathrm{.}314Pa{m}^{3}mo{l}^{-1}{K}^{-1}=0\mathrm{.}08206$ atm L mol $K^{-1}{K}^{-1}$

$1$atm$=1\mathrm{.}01325{10}^{5}Pa$

$1m^3=35\mathrm{.}315f{t}^3$

$(7$ marks$)$