To realize variable water content in state $5$ for an industrial process, the following process is

performed:

An unsaturated humid air $($mass flow of dry air: $m_{L_1}^{}=91\mathrm{.}39k\frac{g}{s})$ is expanded from state $1$

$(p_1=\frac{1\mathrm{.}05}{b}ar,t_1=25C)$ in an adiabatic throttle to $p_2=\frac{1}{b}ar.$ The relative humidity after the

pressure drop is ${}_2=0\mathrm{.}7.$ Another humid air stream $($mass flow of dry air: $m_{L_6}^{}=81\mathrm{.}95\frac{kg}{s},x_6=$

$11\mathrm{.}5\frac{gH{H}_{2}O}{kg*L},t_6=21\mathrm{.}8C)$ flows over a reservoir, absorbing the liquid water mass flow $m_W^{}=132\frac{g}{s}$

$(t_W=15C)$ until the air stream is completely saturated $($state $7).$ The streams $2$ and $7$ are mixed

adiabatically to form stream $3$ and then cooled in an adjustable cooler to the desired state $4.$ The

resulting condensate $(m_c^{}=250\frac{g}{s})$ is discharged to the environment in a droplet seperator and the

dehumidified air sream $($state $5)$ is supplied to the industrial process. The change of state $2$ to $7$ are

isobaric. The condensate and the air stream in $5$ have the same temperature and pressure.

a$)$ Determine the relative humidity ${}_1$ in front of the throttle

b$)$ Determine the temperature of the air stream behind the water reservoir $t_7$

c$)$ Determine the water content $x_3$ after mixing

d$)$ Determine the temperature $t_c$ of the condenstate, which is withdrawn from the process $(5)$

Properties:

Gas constant of dry air: $R_{\text{a}\text{i}\text{r}}=0\mathrm{.}2871\frac{kJ}{kg*K}$

Gas constant of water: $R_W=0\mathrm{.}4615\frac{kJ}{kg*K}$

Specific isobaric heat capacity of dry air: $c_{p,\text{a}\text{i}\text{r}}=1\mathrm{.}007\frac{kJ}{kg*K}$

Specific isobaric heat capacity of liquid water: $c_{p,\text{l}\text{i}\text{q}\text{u}\text{i}\text{d}}=4\mathrm{.}18\frac{kJ}{kg*K}$

Heat of evaporation of water at $0C$:$r_0=2500\frac{kJ}{kg}$

Vapor pressure of water:

Note: All gasneous components can be considered ideal gas