Q$5.$ A blanching operation

In a frozen food production, carrots are to be blanched before the quick$-$freezing operation. The diced carrots are continuously fed to a water blancher, which includes hot water. The carrots exit the system as blanched. With carrots some amount of hot water leaves the system continuously.

It is important to keep the water level in the tank, and water temperature at constant levels.

To be able to keep the water temperature constant at $80C$ in the blancher tank constant, the tank is heated.

To be able to keep the water level constant, the tank has to be also fed with water continuously, since approximately $100k\frac{g}{h}$ of water leaves the system with blanched vegetables.

Q$5.$

Feed: F

Blanched carrots: $P$

Water inlet: $W_{IN}$

Water outlet: W ${?}_{\text{O}\text{U}\text{T}}$

The feed $(F)=500k\frac{g}{h}$

Carrot $C{p}_{\text{a}\text{v}\text{g}}=3\mathrm{.}8k\frac{J}{k}gDC$

Water $C{p}_{\text{a}\text{v}\text{g}}=4\mathrm{.}18k\frac{J}{k}gDC$

$T_{\text{i}\text{n}\text{l}\text{e}\text{t}}$ of water $=15C$

$T_{\text{i}\text{n}\text{l}\text{e}\text{t}}$ of carrots $=20C$

$T_{\text{o}\text{u}\text{t}\text{l}\text{e}\text{t}}$ of carrots $=65C$

Calculate the amount of heat supply $($kWh$)$ to the system to keep the water temperature constant.