We wish to flash distill an ethanol$-$water mixture that is $30\mathrm{.}0wt\%$ ethanol and has a feed flow of $1000k\frac{g}{h}.$ Feed is at $200\mathrm{.}0C,$ and remains liquid at a high pressure. The flash drum operates at a pressure of $1\mathrm{.}0k\frac{g}{c}{m}^2.$ Find $T_{\text{d}\text{r}\text{u}\text{m}\text{,}}$ weight fraction of liquid and vapor products, and liquid and vapor flow rates.

Data:

$C_{PL,\text{E}\text{t}\text{O}\text{H}}=37\mathrm{.}96,$kca$\frac{l}{\text{k}\text{m}\text{o}\text{l}C}$

$C_{PL\text{w}\text{a}\text{t}\text{e}\text{r}}=18\mathrm{.}0,$kca$\frac{l}{\text{k}\text{m}\text{o}\text{l}C}$

$C_{PV\text{E}\text{t}\text{o}\text{H}}=14\mathrm{.}66+3\mathrm{.}758{10}^{-2}T-2\mathrm{.}091{10}^{-5}{T}^2+4\mathrm{.}74{10}^{-9}{T}^3$

$C_{PV\text{w}\text{a}\text{t}\text{e}\text{r}}=7\mathrm{.}88+0\mathrm{.}32{10}^{-2}T-0\mathrm{.}04833{10}^{-5}{T}^2$

Both $C_{PV}$ values are in kca$\frac{l}{\text{k}\text{m}\text{o}\text{l}C},$ with $T$ in $C.$

${}_{\text{E}\text{t}\text{O}\text{H}}=0\mathrm{.}789\frac{g}{mL},{}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1\mathrm{.}0\frac{g}{mL},M{W}_{\text{E}\text{t}\text{O}\text{H}}=46\mathrm{.}07\frac{g}{\text{m}\text{o}\text{l}},M{W}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=18\mathrm{.}016\frac{g}{\text{m}\text{o}\text{l}}$

${}_{\text{E}\text{t}\text{O}\text{H}}=9\mathrm{.}22\frac{\text{k}\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}}at351\mathrm{.}7K,$ and ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=9\mathrm{.}7171\frac{\text{k}\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}}at373\mathrm{.}16K$

Enthalpy composition diagram at $p=1k\frac{g}{c}{m}^2$ is in Fig. $1$ below. Note: Be careful with units.

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Enthalpy composition diagram at $p=1k\frac{g}{c}{m}^2$ is in Fig. $1$ below. Note: Be careful with units.

Fig. $1,$ Enthalpy$-$composition diagram for ethanol$-$water at a pressure of $1k\frac{g}{c}{m}^2$