Question

Dew Point If the air temperature is \(25^{\circ} \mathrm{C}\) and the relative humidity is 55 percent, will the dew point be reached if the temperature drops to \(20^{\circ} \mathrm{C}\) ?

Short answer

No, the dew point of 16°C will not be reached if the air cools to 20°C.

Step-by-step solution

Understanding the Dew Point

The dew point is the temperature at which air becomes saturated with moisture and water vapor begins to condense into dew. If the air temperature falls to this level or below, dew formation can occur.

Applying the Dew Point Formula

To estimate the dew point, we use the approximation formula: \( T_d = T - \left(\frac{100 - RH}{5}\right) \), where \( T_d \) is the dew point, \( T \) is the air temperature, and \( RH \) is the relative humidity. Inserting the values: \( T = 25^{\circ} \mathrm{C} \), \( RH = 55\% \).

Calculate Dew Point

Substitute the given values into the formula: \[ T_d = 25 - \left(\frac{100 - 55}{5}\right) \] Simplifying, \[ T_d = 25 - \left(\frac{45}{5}\right) = 25 - 9 = 16^{\circ} \mathrm{C} \]. Thus, the dew point temperature is \( 16^{\circ} \mathrm{C} \).

Compare Dew Point and Final Temperature

The dew point temperature is \( 16^{\circ} \mathrm{C} \). If the air temperature drops to \( 20^{\circ} \mathrm{C} \), it will not reach the dew point of \( 16^{\circ} \mathrm{C} \). No dew will form as the air has not cooled sufficiently to reach the dew point.

Key concepts

Relative Humidity

Relative humidity is a measure of how much moisture is in the air compared to how much the air could potentially hold at a given temperature. It's expressed as a percentage. For example, at 55% relative humidity, the air contains 55% of the maximum moisture it could hold before getting saturated.

• Relative humidity varies with temperature: as the air temperature changes, the amount of moisture it can hold also changes.
• Warm air can hold more moisture than cool air; thus, relative humidity may increase or decrease with temperature changes even if the actual amount of moisture in the air stays the same.

Understanding relative humidity is crucial when calculating the dew point, as it's one of the key variables in determining at what temperature dew will form.

Condensation

Condensation is the process through which water vapor in the air is converted into liquid water. This often happens when warm, moist air comes into contact with a cool surface, causing the moisture to cool and change state.

• This occurrence is frequent when the temperature drops to the dew point, which is the critical temperature at which air becomes fully saturated with water vapor.
• Common examples include dew on grass in the morning or droplets on a cold bottle.

Understanding condensation is important in meteorology and daily life, as it helps us to predict weather patterns and manage moisture levels indoors to avoid dampness and mold. Condensation requires that the air cools sufficiently, often occurring typically at night or when the air comes in contact with cooler surfaces.

Air Temperature

Air temperature is a fundamental factor influencing weather patterns and determining how much moisture the air can hold. It's the measure of how hot or cold the air is, often recorded in degrees Celsius or Fahrenheit.

• Air temperature affects relative humidity: as the air warms, its capacity to hold water increases, lowering relative humidity and delaying condensation unless additional moisture is added.
• Conversely, when the air cools down, its ability to hold water decreases, increasing relative humidity and enhancing the likelihood of reaching the dew point.

In our exercise, the air temperature dropping from 25°C to 20°C is vital to examine whether this drop is enough to reach the dew point of 16°C, which it turns out, isn't. However, understanding how air temperature and dew point interact is key to forecasting whether conditions are ripe for dew or precipitation. By realizing these relationships, we gain insights into the very fabric of weather forecasting.