A chilled-water heat-exchange unit is designed to cool $5 \mathrm{~m}^{3} / \mathrm{s}$ of air at $100 \mathrm{~kPa}$ and $30^{\circ} \mathrm{C}$ to $100 \mathrm{~kPa}$ and $18^{\circ} \mathrm{C}$ by using water at $8^{\circ} \mathrm{C}$. Find the maximum water outlet temperature when the mass flow rate of the water is $2 \mathrm{~kg} / \mathrm{s}$.

Solution

Verified**Given data**:

$P_1=100 \; \text{kPa}$ $\dot{v}_1=5 \; \frac{\text{m}^3}{\text s}$ $T_1=30^{\circ} \; \text C \to 303.15 \; \text K$

$P_2=100 \; \text{kPa}$ $T_2=18^{\circ} \; \text C$

$T_w=8 ^{\circ} \; \text C$

$\dot{m}_w=2\; \frac{\text{kg}}{\text s}$ $c_w=4.18 \; \frac{\text{kJ}}{\text{kg \; K}}\\$

$T_{2w}=?$

We have a **steady flow** process. We will use TABLES to find missing properties. We will show how to apply **First Law** and **Law of Conservation of mass** in the equations. We must be careful not to mistake what our **control volume** is.

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