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Relative humidity is a measure of how much moisture the air currently holds compared to the maximum amount it could hold at a particular temperature. It is expressed as a percentage.
To understand it better, think of a sponge: a completely soaked sponge represents 100% relative humidity, whereas a damp sponge represents less. Relative humidity can be calculated using the formula:\[\text{Relative Humidity} = \left( \frac{\text{Actual Vapor Pressure}}{\text{Saturation Vapor Pressure}} \right) \times 100\%\]This formula shows the relationship between the partial pressure of the water vapor currently in the air (or actual vapor pressure) and the vapor pressure at saturation (maximum, at a specific temperature).

• If the relative humidity is 100%, it means the air is fully saturated with water vapor and can't hold more without some condensing, like dew or rain.
• A lower percentage means the air is drier.

In the problem above, when the temperature changes but the partial pressure of water remains the same, the relative humidity changes based on its current capacity to hold moisture.

Atmospheric pressure (also known as air pressure) is the force exerted by the weight of the air above a surface. It is an important concept in understanding how weather and climate work.
The atmospheric pressure is measured in units like pascal (Pa) or atmospheres (atm).It can be different based on location and elevation:

• At sea level, the standard atmospheric pressure is about \(1.013 \times 10^5\) Pa (or 1013 hPa or 1 atm).
• It decreases with higher altitude because there is less air above.

In the context of our exercise, knowing the atmospheric pressure helps in understanding the proportion that water vapor pressure constitutes at different temperatures. Remember, water vapor contributes to the total air pressure, and when relative humidity reaches 100%, the vapor pressure equals the partial pressure of the water vapor.

Partial pressure is the pressure contributed by a single type of gas in a mixture of gases. When we talk about air, it's made up of several gases like nitrogen, oxygen, and water vapor among others.
In atmospheric science, partial pressures are pivotal in understanding the behavior and proportionate contribution of each gas to the total atmospheric pressure.To calculate the partial pressure of a gas in a mixture, we use the formula:\[P_{i} = \frac{n_{i}}{n_{\text{total}}} \times P_{\text{total}}\]where \(P_{i}\) is the partial pressure of the gas, \(n_{i}\) is the number of moles of the gas, \(n_{\text{total}}\) is the total number of moles, and \(P_{\text{total}}\) is the total pressure of the gas mixture. For example:

• The partial pressure of water vapor at \(10^\circ C\) in our problem was \(1300 \text{ Pa}\), forming a small part of the total atmospheric pressure.
• In cases of 100% relative humidity, the actual vapor pressure equals the saturation vapor pressure, making partial pressure calculations straightforward in such scenarios.

Understanding partial pressure allows us to see how each component of the air affects overall pressure, crucial for fields like meteorology and climate science.