When manufacturing isobutene from $n-$butane, the first step of the process is to compress the $n-$butane. In a particular plant, the $n-$butane is compressed from $0\mathrm{.}95$MPa and $80C$ to $1\mathrm{.}89$MPa and $120C.$ The compressor receives $2100\frac{J}{m}ol.$ Starting from the first law, find the equation the calculate the heat that must be supplied per mole of $n-$butane. Then use the Pitzer generalized correlation for $z$ to calculate the enthalpy departure values, along with the MCPH values below to calculate the needed heat.

Constants:

$T_c=425\mathrm{.}16K,P_c=3\mathrm{.}796$MPa,$=0\mathrm{.}197,A=1\mathrm{.}935,B=0\mathrm{.}0369K^{-1},C=-1\mathrm{.}14{10}^{-5}{K}^{-2}$