$3\mathrm{.}4.$ A distillation column with a total condenser is shown in Fig. $3\mathrm{.}3.$

The system to be studied in this problem has an average enthalpy of

vaporization of $32k\frac{J}{m}ol,$ an average $C_P^L$ of $146\frac{J}{m}ol-C,$ and an

average $C_P^V$ of $93\frac{J}{m}ol-$C$.$ Variable names for the various stream

flow rates and the heat flow rates are given in the diagram. The feed

can be liquid, vapor, or a mixture represented using subscripts to

indicate the vapor and liquid flows, $F=F_V+F_L.$ The enthalpy flow

due to feed can be represented as: for saturated liquid, $F_L{H}^{\text{s}\text{a}\text{t}\text{L}}$; for

saturated vapor, $F_V{H}^{\text{s}\text{a}\text{t}\text{V}}$; for subcooled liquid, $F_L{H}^{\text{s}\text{a}\text{t}\text{L}}+F_L{C}_P^L(T_F\}$

$\{$:$T^{\text{s}\text{a}\text{t}\text{L}})$; for superheated vapor, $F_V{H}^{\text{s}\text{a}\text{t}\text{V}}+F_V{C}_P^V(T_F-T^{\text{s}\text{a}\text{t}\text{V}})$; and for a

mix of vapor and liquid, $F_L{H}^{\text{s}\text{a}\text{t}\text{L}}+F_V{H}^{\text{s}\text{a}\text{t}\text{V}}.$

a$.$ Use a mass balance to show $F_V+V_S-V_R=L_S-L_R-F_L.$

d$.$ For subcooled liquid feed, $F_V=0.$ Show $V_R-V_S=$

$F_L{C}_P\frac{T_F-T^{\text{s}\text{a}\text{t}}}{}{H}^{\text{v}\text{a}\text{p}}.$

g$.$ Use the mass and energy balances around the total

condenser to relate the condenser duty to the enthalpy of

vaporization, for the case of streams $L_R$ and $D$ being

saturated liquid.

h$.$ Use the mass and energy balances around the reboiler to

relate the reboiler duty to the enthalpy of vaporization.

$[$For parts $($j$)-($o$),$ find all other flow rates and heat

exchanger duties $(Q$ values$).]$

n$.$ subcooled liquid$),D=53,\frac{L_R}{D}=$

$2\mathrm{.}5.$