91Ó°ÊÓ

Relative humidity is a measurement of the amount of water vapor present in the air compared to the maximum amount of vapor the air can hold at a given temperature. It is expressed as a percentage.
To calculate relative humidity, you need to understand the concept of saturation. Saturation occurs when the air holds as much water vapor as it can at a specific temperature. This is known as the saturation vapor pressure.
When the relative humidity is 100%, it means the air is fully saturated with water vapor. If the air's temperature decreases or the water vapor increases further, condensation can occur. This is how dew or fog forms.
To calculate relative humidity, use the formula:

• \( \text{Relative Humidity} = \left(\frac{\text{Actual Vapor Pressure}}{\text{Saturation Vapor Pressure}}\right) \times 100 \) %

In our problem, at \( 35^{\circ} \text{C} \), the saturation vapor pressure is \( 5500 \text{ Pa} \) and the actual vapor pressure remains at \( 1300 \text{ Pa} \), leading to a relative humidity of \( 23.64\% \).

Partial pressure refers to the pressure exerted by each individual gas in a mixture of gases. In any mixture, each gas contributes to the total pressure of the mixture based on its own presence or abundance in that mixture.
This concept is crucial in understanding how gases behave when mixed. For example, in our atmosphere, nitrogen, oxygen, water vapor, and other gases each have their own partial pressures.
The total pressure of the air is the sum of all the partial pressures of the gases within it. This is described by Dalton's Law of Partial Pressures, which states:

• \( P_{\text{total}} = P_{1} + P_{2} + ... + P_{n} \)

For the water vapor, when relative humidity is 100%, its partial pressure equals the vapor pressure of water at that temperature. Therefore, at \( 10^{\circ} C \), the partial pressure of the water vapor is \( 1300 \text{ Pa} \).

Atmospheric pressure is the total pressure exerted by the atmosphere at a given point. It is the force per unit area exerted by air on the surface due to gravity.
Measured in pascals (Pa), it varies based on altitude, temperature, and weather conditions, but at sea level, it is generally around \( 101325 \text{ Pa} \), or \( 1.013 \times 10^5 \text{ Pa} \).
This pressure affects weather patterns and influences how we measure other properties of gases, such as vapor pressure.
In our exercise, atmospheric pressure was considered to be \( 1.013 \times 10^5 \text{ Pa} \), providing a basis for comparing vapor pressure and calculating relative humidity.