$1$a$)$ During the Spray dryer demonstration, $34\mathrm{.}6$ gram of fresh egg white was pumped into the spray dryer, and at the end of the drying process, $4\mathrm{.}2$ gram of dried egg white powder was collected. Calculate the solids weight fraction $($Ws$)$ of the initial $($fresh$)$ egg white before drying. $*$Neglect the amount that is not collected. Assume the initial and final moisture contents of egg white to be $90\%$ and $4\%($wet basis$),$ respectively. b$)$ If the change in enthalpy of the fresh egg in $3$a$)$ during the warmup period is $60$ kJ$/$kg$.$ Calculate the heat gain Qegg. $($use equation below$)$ c$)$ Determine the spray dryer thermal efficiency $($E$)$ and the heat losses $($L$)$ in $\%$ given that: Latent heat of vaporization of water during drying $=2357\mathrm{.}7$ kJ$/$kg$,$ total drying time $=5$ min, and Aspirator dial set A $=15.($use the equation below$)$ d$)$ Determine the spray dryer thermal efficiency $($E$)$ and the heat losses $($L$)$ in $\%$ given that: Latent heat of vaporization of water during drying $=2357\mathrm{.}7$ kJ$/$kg$,$ total drying time $=40$ min, and Aspirator dial set A $=30.($use the equation below$)$

a$)$ Determine $H_r$ and $H_0$

Note: $H_r=H_i$

b$)$ Determine $i_r,i_i$ and $i_o$

Note: $H_r=H_i$

c$)$ Use the psychrometric chart to determine the outlet wet bulb temperature $T_{wb,o}$ Note: $H_r=H_i$ and $T_O$ and $T_{wb,o}$ are on the same enthalpy line.

The egg is assumed to be warmed up from $20C$ to $T_{wb,o}$ before evaporation occurs.

d$)$ Evaluate $,Q_{\text{e}\text{g}\text{g}}=(x_i)(i_{w,wb,o}-i_{w,20}C)($mass of egg white pumped to the drier$)$

$Q_P=*m_w$

$Q_R=m_{d\text{e}\text{g}\text{g}}**C_{p\text{e}\text{g}\text{g}\text{p}\text{o}\text{w}\text{d}\text{e}\text{r}}**(T_o-T_{wb,o})=m_{d,\text{e}\text{g}\text{g}}**1\mathrm{.}67k\frac{J}{k}gC**(T_o-T_{wb,o})$

where: $Q_{\text{e}\text{g}\text{g}}$ is heat gain by total egg in warm up period

$i_{w,wb,o}$ is the enthalpy of liquid water at the wet bulb temperature of outlet air stream and $1$atm pressure $($use steam table$)$

$i_{w,20C}$ is the enthalpy of liquid water at $20C$ and $1$atm pressure $($use steam table$)x_i$ is the initial moisture content of the egg white in wet basis $($e$.$ g$.0\mathrm{.}9)$

$Q_p$ is heat utilized to evaporate water

$$ is the latent heat of evaporation of water during drying.

$m_w=$ mass of water evaporated

$Q_R$ is heat gained by total egg during drying process $m_{d,\text{e}\text{g}\text{g}}$ is the mass of the dried egg white powder collected $C_p,$ egg powder is the specific heat capacity of egg white powder

e$)$ Determine the amount of heat supplied:

$Q_{\text{t}\text{o}\text{t}}=(i_i-i_r)(massof$ air used during drying$)$

Note: air flow rate $(k\frac{g}{s})=5\mathrm{.}64{10}^{-4}(A)-1\mathrm{.}02{10}^{-5}(A{)}^2$

where: $A=$ aspirator dial set $=15$

Mass of air $=$ air flow rate $**$

f$)$ Determine the thermal efficiency $($E$)$ and the heat losses $($L$)$ in $\%$ value