The products of combustion are flowing through a heat...

The products of combustion are flowing through a heat exchanger with $12 \% \mathrm{CO}_{2}, 13 \% \mathrm{H}_{2} \mathrm{O},$ and $75 \% \mathrm{N}_{2}$ on a volume basis at the rate $0.1 \mathrm{kg} / \mathrm{s}$ and $100 \mathrm{kPa}$. What is the dew-point temperature? If the mixture is cooled $10^{\circ} \mathrm{C}$ below the dew-point temperature, how long will it take to collect $10 \mathrm{kg}$ of liquid water?

Key Concepts

Dew Point Temperature

This is the temperature at which a gas mixture becomes saturated with water vapor and condensation starts to occur. It is determined by the water vapor pressure in the mixture matching the saturation pressure of water at that temperature. In many engineering calculations, it is a key parameter for understanding when and how vapor will condense into liquid in heat exchangers or other equipment.

Partial Pressure

Partial pressure refers to the pressure that each component of a gas mixture would exert if it were alone in the container at the same temperature. When dealing with humid gases, the water vapor’s partial pressure is found by multiplying its mole (or volume) fraction by the total pressure, and this value is fundamental to determining the dew point.

Ideal Gas Law in Gas Mixtures

The ideal gas law relates the pressure, volume, temperature, and amount of gas, and it is often applied to each component in a gas mixture. Because volume fractions for gases in an ideal mixture are equivalent to mole fractions, the law allows for the determination of individual component pressures and subsequent thermodynamic properties.

Mass and Mole Fractions

In multicomponent systems, distinguishing between mole (or volume) fractions and mass fractions is essential. While volume fractions are directly related to mole fractions in ideal gases, converting these to mass fractions using molecular weights is necessary for performing mass balance calculations such as determining the accumulated condensed water mass.

Condensation and Accumulation Calculations

When a gas mixture is cooled below its dew point, water vapor begins to condense. Determining the amount of condensation involves calculating the difference in vapor content before and after cooling using the known saturation properties. This condensation rate, combined with the overall mass flow rate, is used to compute how long it takes to collect a given mass of liquid water, which is critical in designing and evaluating heat exchanger performance.

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