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 $32$ kJ$/$mol$,$ an average of $146$ J$/$mol$\backslash$deg $-$C$,$ and an

average of $93$ J$/$mol$\backslash$deg $-$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 $=$ FV $+$ FL

$.$ The enthalpy flow

due to feed can be represented as: for saturated liquid, FLHsatL

; for

saturated vapor, FVHsatV

; for subcooled liquid, FLHsatL $+$ FLCP

L

$($TF $$

T

satL

$)$; for superheated vapor, FVHsatV $+$ FVCP

V

$($TF $$ T

satV

$)$; and for a

mix of vapor and liquid, FLHsatL $+$ FVHsatV

$.$

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

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

e$.$ For superheated vapor feed, $F_L=0.$ Show $L_S-L_R=$

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

f$.$ For a feed mixture of saturated liquid and saturated vapor.

Show $V_R=V_S+F_V,L_S=L_R+F_L.$

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

relate the reboiler duty to the enthalpy of vaporization.