A liquid with a molar composition of $60\%$ benzene and $40\%$ toluene at $20C$ is

evaporated in a partial evaporator at a constant temperature of $50C$ under

vacuum. The vapor and liquid streams leaving the evaporator are in equilibrium

and the molar composition of benzene in the vapor stream is $68\mathrm{.}4\%$ and the

molar composition of the benzene in the liquid stream is $40\%.$ Calculate the

heat $(k\frac{J}{k}$mol$)$ that must be supplied to the evaporator per kilomole of the feed.

$Cp$ Benzene $(l)=62\mathrm{.}55+23\mathrm{.}4{10}^{-2}T,T$: Kelvin

$Cp$ Toluene $(l)=165k\frac{J}{k}$molK

$Cp$ Benzene $(v)=74\mathrm{.}06+32\mathrm{.}95{10}^{-2}T-25\mathrm{.}2{10}^{-5}{T}^2,T$: Celcius

$Cp$ Toluene $(v)=94\mathrm{.}18+38{10}^{-2}T-27\mathrm{.}86{10}^{-5}{T}^2,T$: Celcius