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$(25$ points$)$ Consider $m=1Kg$ of nitrogen $($ N $2)$ gas being compressed within the reduced pressure range $5P_{n}6\mathrm{.}5$ in a rigid tank at $164C.$ Assume that the compressibility factor $Z$ has presed reduced pressure range under these conditions as shown in the

$4\mathrm{.}1$ The compressibility factor equation is defined by $Z=0\mathrm{.}55+0\mathrm{.}0236P.$

True $$ False $$

$4\mathrm{.}2$ For compressing nitrogen $(N_2)$ gas isothermally at $164C,$ the work done expression is defined by $W=0\mathrm{.}55mRThn(\frac{P_1}{P_2}).$

True $$ False $$

$4\mathrm{.}3$ The corresponding pressures at states $1$ and $2$ are $P_1=16\mathrm{.}95$MPa and $P_2=22\mathrm{.}04$MPa.

True $$ False $$

$4\mathrm{.}4$ The corresponding specific volumes are $v_1=0\mathrm{.}002870\frac{m^3}{K}g$ and $v_2=0\mathrm{.}002209\frac{m^3}{K}g$ True False $$

$4\mathrm{.}5$ Finally, the work done for compressing nitrogen is $W=-8\mathrm{.}23kJ.$ False

$4$