Question

When the room temperature becomes equal to the dew point the relative humidity of the room is (A) \(100 \%\) (B) \(0 \%\) (C) \(70 \%\) (D) \(85 \%\)

Short answer

When the room temperature becomes equal to the dew point, it means the air is saturated and cannot hold any more moisture. In this situation, the relative humidity is \(100\%\), as the partial pressure of water vapor is equal to the saturation vapor pressure. So, the correct answer is (A) \(100\%\).

Step-by-step solution

Understand Relative Humidity

Relative humidity (RH) is a measure of how full of water vapor the air is relative to the maximum amount of water vapor the air can hold at a given temperature. It is expressed as a percentage and calculated using the formula: \(Relative\ Humidity = \frac{Partial\ Pressure\ of\ Water\ Vapor}{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature} \times 100\%\)

Understand Dew Point

The dew point is the temperature at which the air is saturated, meaning it has reached its maximum capacity to hold moisture. If the air temperature cools further, the excess moisture will condense out as precipitation or dew.

Calculate Relative Humidity at Dew Point

When the room temperature becomes equal to the dew point, it means the air is saturated, and the partial pressure of water vapor is equal to the saturation vapor pressure. Putting this information into the relative humidity formula: \(Relative\ Humidity = \frac{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature}{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature} \times 100\% = 100\%\)

Finding the Answer

Since the relative humidity when the room temperature becomes equal to the dew point is 100%, the correct answer is: (A) \(100\%\)

Key concepts

Dew Point

The dew point is a fundamental concept in understanding weather and humidity. It is the temperature at which air becomes fully saturated with water vapor. Once air reaches this temperature, it cannot hold any more moisture, leading to the formation of dew.

When the air cools to the dew point, the water vapor starts condensing into tiny droplets, which you see as dew on grass or windows. Dew point varies depending on the amount of moisture in the air; higher dew points mean more moisture.

In essence, the dew point helps us understand how "humid" the air feels. A higher dew point feels clammy and sticky, while a lower dew point feels more comfortable. Knowing the dew point can help predict foggy conditions or potential frost overnight.

Saturation Vapor Pressure

Saturation vapor pressure refers to the pressure exerted by water vapor when a body of water is in equilibrium with its surrounding vapor. This pressure changes with temperature; warmer air can hold more moisture, leading to higher saturation vapor pressures.

This is crucial for understanding humidity and moisture content in the air. As the temperature increases, the air's capacity to contain water vapor does too.

At the dew point, the actual amount of water vapor matches the saturation vapor pressure. Knowing this relationship is key for meteorologists and helps us explain the hygrometer readings in weather forecasts.

To visualize this, think of a sponge absorbing water. The warmer the environment, the more "water" the sponge can hold before it drips.

Water Vapor

Water vapor is the gaseous form of water and a vital part of the Earth's atmosphere. It plays a key role in the weather, climate, and the water cycle.

When water evaporates, it turns into water vapor. This process involves the conversion of liquid water into gas. As the air becomes filled with water vapor, it approaches its saturation point. This is crucial for forming clouds, fog, and even precipitation.

Understanding water vapor is essential for grasping how weather patterns work. When it reaches the dew point, excess water vapor begins to condense, leading to dew or rain.

It's also a potent greenhouse gas, contributing to the natural warming of our planet by trapping heat.

Temperature

Temperature is a measure of heat energy in the environment and plays a significant role in determining weather conditions and human comfort. It affects the capacity of the air to hold water vapor.

When considering relative humidity, temperature is essential. As temperatures rise, so does the potential for air to hold more moisture.

Conversely, a drop in temperature may lead the air to reach its saturation, or dew point, resulting in condensation.

Monitoring temperature allows us to prepare for weather changes. It's why meteorologists keep a close eye on temperature trends: to predict dew points, fog, frost, or heatwaves. Without a clear understanding of temperature, predicting humidity or weather becomes very challenging.