A room is filled with saturated moist air at 25^∘ C and a total pressure of 100 kPa. If the mass

step 1 Problem 140. In this problem in the room there is air and the total pressure inside the room is

A room is filled with saturated moist air at 25^∘ C and a...

A room is filled with saturated moist air at $25^{\circ} \mathrm{C}$ and a total pressure of $100 \mathrm{kPa}$. If the mass of dry air in the room is $100 \mathrm{kg},$ the mass of water vapor is $(a) 0.52 \mathrm{kg}$ $(b) 1.97 \mathrm{kg}$ $(c) 2.96 \mathrm{kg}$ $(d) 2.04 \mathrm{kg}$ $(e) 3.17 \mathrm{kg}$

A room is filled with saturated moist air at $25^{\circ} \mathrm{C}$ and a total pressure of $100 \mathrm{kPa}$. If the mass of dry air in the room is $100 \mathrm{kg},$ the mass of water vapor is
$(a) 0.52 \mathrm{kg}$
$(b) 1.97 \mathrm{kg}$
$(c) 2.96 \mathrm{kg}$
$(d) 2.04 \mathrm{kg}$
$(e) 3.17 \mathrm{kg}$

Key Concepts

Application of the Ideal Gas Law

The ideal gas law relates the pressure, temperature, volume, and amount of gas, and is used as an approximation for both dry air and water vapor under many conditions. This allows for the computation of properties such as partial pressures and mass from known state variables, which is fundamental in solving moist air problems.

Saturation and Saturated Conditions

Saturation refers to the state when air contains the maximum amount of water vapor possible at a given temperature, meaning that any additional moisture will not be absorbed without condensation. Understanding this concept is essential when analysing scenarios involving saturated air, where the water vapor pressure equals the saturation pressure.

Dalton's Law of Partial Pressures

This law states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures contributed by each individual gas. In moist air problems, it is used to separate the partial pressure of water vapor from that of dry air, which is crucial for determining properties such as the humidity ratio.

Humidity Ratio

The humidity ratio, or moisture content, is defined as the mass of water vapor per unit mass of dry air. This parameter is central in the study of moist air (psychrometrics), enabling the quantification of the water content in air, and is used in calculations that involve air conditioning and atmospheric processes.

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