In an air conditioning system, moist air passes through three different states:

State $1($inlet$)$:

$-$ Temperature: $28\backslash$deg C

$-$ Pressure: $1$ bar

$-$ Relative Humidity: $0\mathrm{.}7$

Between States $1$ and $2,$ a cooling process occurs, with a heat exchange given by dQ$/$dT $=-38\mathrm{.}9$ kW$.$

State $2($cooling coil$)$:

$-$ Temperature: to be determined $($T $=?)$

$-$ Pressure: $1$ bar

$-$ Relative Humidity: $1$

$-$ The water temperature in state $2$ equals the temperature of the wet vapor.

Between States $2$ and $3,$ the moist air undergoes a heating process.

State $3($humidifier$)$:

$-$ Temperature: $24\backslash$deg C

$-$ Pressure: $1$ bar

$-$ Relative Humidity: $0\mathrm{.}4$

Given that:

$-$ The gravitational acceleration $($g$)$ is $9\mathrm{.}81$ m$/$s$^2,$

$-$ The molar mass of water is $18$ g$/$mol$,$ and the molar mass of dry air is $28\mathrm{.}97$ g$/$mol$,$

$-$ Moist air consists of water vapor and dry air,

Questions:

$1.$ Calculate the water vapor pressure $($H$$O$)$ in the moist air at the inlet.

$2.$ Determine the specific mass of H$$O in moist air at the inlet $($Calculate in M$/$V$).$

$3.$ Calculate the specific mass of dry air in the moist air at the inlet.

$4.$ Determine the specific volume of moist air at the inlet.

$5.$ Calculate the volumetric enthalpy of moist air at the inlet.

$6.$ Determine the specific enthalpy of moist air at the inlet.

$7.$ Calculate the water vapor pressure $($H$$O$)$ in moist air at the outlet of the humidifier.

$8.$ Determine the specific mass of H$$O in moist air at the humidifier outlet.

$9.$ Calculate the specific mass of dry air in moist air at the humidifier outlet.

$10.$ Determine the specific enthalpy of moist air at the outlet of the humidifier.

$11.$ Calculate the specific volume of moist air at the humidifier outlet.

$12.$ Determine the volumetric enthalpy of moist air at the humidifier outlet.

$13.$ Calculate the specific enthalpy of moist air at the coil outlet.

$14.$ Knowing that the moist air at the outlet of the cooling coil contains the same H$$O content as dry air, and the moist air is saturated, use the P$/$T relation to calculate the exit temperature of the cooling coil.

$15.$ Determine the volumetric enthalpy of moist air exiting the cooling coil.

$16.$ Calculate the specific enthalpy of moist air exiting the cooling coil.

$17.$ Calculate the mass flow rate of moist air at the inlet.

$18.$ Determine the mass flow rate of condensed H$$O exiting the cooling coil.

$19.$ Calculate the heat exchange rate of moist air exiting the cooling coil with the heating coil.