Exercise $3$

In the refrigerator laboratory of a testing institute, a climatic chamber is operated in water

energy consumption measurements are carried out on refrigerators. In order to maintain the

conditions required for a so$-$called standard energy consumption measurement, a temperature

of ${}_N=25C$ and a relative humidity of ${}_N=60\%$ must be kept constant at a height next

the appliances $($see sketch$).$ The climatic chamber is perfectly insulated except for the flow

through which a constant heat flux $Q_{\text{F}\text{l}\text{o}\text{o}\text{r}}^{}=200W$ escapes, since the climatic chamber

located in the basement and the floor has a temperature of ${}_{\text{F}\text{l}\text{o}\text{o}\text{r}}=20C.$ During a running

measurement, there are $N_{KG}=8$ refrigerator cooling units in the chamber, each of which emit

an average heat flux of $Q_{KG}^{}=50W$ to the chamber air. The chamber air conditioning system

sucks in air to be conditioned near the floor, which has cooled to a temperature of ${}_1=24$

due to heat loss via the chamber floor. Of the intake air mass flow, $20\%$ is replaced by free

air, which on a summer day has a temperature of ${}_F=30C$ and a relative humidity of ${}_F$

$70\%.$ Subsequently, the mixed air is cooled in a heat exchanger by a tempered brine, with

temperature of ${}_{\text{B}\text{r}\text{i}\text{n}\text{e}}=10C.$ The water condensed out of the air during cooling is completly

separated. Subsequent to the dehumidification process a downstream heater finally brings the

air to the required inlet temperature of ${}_4=22C$ supplying the heat flow $Q_{\text{H}\text{e}\text{a}\text{t}\text{i}\text{n}\text{g}}^{}.$

$1)$ Calculate the mass flow of dry air $m_1^{}$ so that

constante temperature condition are maintained in the

climatic chamber?

$2)$ calculate the temperature ${}_2$ and relative humidity

$Q_2$ after mixing the air steams?

$3)$ calculate the temperature the air must be cooled

to be dehumidification?

$4)$ calculate the heat flux Qwu absorbed by Brine

in the heat exchanger to cool the air down to

the dehumidification temperature ${}_2$ which

mas flow rate $m_w^{}$ must be removed when

dehumidifyning the air?

$5)$ catculate the heat flow of the heater QHeating

by which the air is bought to the inlet

temperature ${}_4=22C$ after dehumidification Material data:

all changes of state of humid are performed

at $p=1\mathrm{.}01325$ bar

specific isobaric heat capacities:

$C_{p\text{a}\text{i}\text{r}}=1\mathrm{.}004\frac{KJ}{kg*K}$

$C_{p(water)\text{V}\text{a}\text{p}\text{o}\text{r}}=1,86\frac{KJ}{kgK}$

$C_{p(water)\text{L}\text{i}\text{q}\text{u}\text{i}\text{d}}=4,186\frac{KJ}{KgK}$

Specific gas constants:

$R_{\text{a}\text{i}\text{r}}=0\mathrm{.}2871\frac{KJ}{KgK},R_{\text{w}\text{a}\text{t}\text{e}\text{r}}=0\mathrm{.}46151\frac{KJ}{KgK}$

Enthalpy of Vaporization of water at $0C=$

$h_y=2500\frac{kJ}{ky}$

Vapor pressure curve of water:

$ln(\frac{P}{P_0})=12,41682-4222,037\frac{K}{T-31,95K}$

with $T$ in $K$ and $P_0=1$ bar