On a day when the air temperature is 75°F, the relative humidity is measured to be 86%. How many degrees would the air temperature have to be lowered for the relative humidity to be 100%?
To find out how many degrees the air temperature would need to be lowered for the relative humidity to reach 100%, we need to understand the concept of dew point temperature. The dew point temperature is the temperature at which the air becomes saturated with water vapor, leading to the formation of dew or fog.
To calculate the dew point temperature, we can use the following formula:
Td = T - ((100 - RH) / 5)
Where:
Td is the dew point temperature
T is the air temperature in Celsius
RH is the relative humidity in percent
First, let's convert the air temperature from Fahrenheit (°F) to Celsius (°C):
T = (75°F - 32) × 5/9
T ≈ 23.9°C
Now, let's substitute the values into the formula:
Td = 23.9 - ((100 - 86) / 5)
Td = 23.9 - (14 / 5)
Td ≈ 21.6°C
Therefore, the dew point temperature at a relative humidity of 86% is approximately 21.6°C.
To find the temperature at which the relative humidity would reach 100%, we need to find the difference between the current temperature and the dew point temperature:
Temperature Difference = T - Td
Temperature Difference = 23.9°C - 21.6°C
Temperature Difference ≈ 2.3°C
Therefore, the air temperature would need to be lowered by approximately 2.3 degrees Celsius for the relative humidity to reach 100%.
To determine how many degrees the air temperature would have to be lowered for the relative humidity to be 100%, we need to understand the relationship between temperature and relative humidity.
Relative humidity is a measure of how saturated the air is with moisture, expressed as a percentage of the maximum amount of moisture the air can hold at a given temperature.
Step 1: Find the dew point temperature
To calculate the dew point temperature, we can use the following formula:
dew point temperature = air temperature - ((100 - relative humidity) / 5)
In this case, the air temperature is 75°F, and the relative humidity is 86%.
dew point temperature = 75°F - ((100 - 86) / 5) = 70.8°F (rounded to the nearest tenth)
Step 2: Calculate the temperature difference needed for 100% relative humidity
To determine how many degrees the air temperature would have to be lowered for the relative humidity to be 100%, we subtract the dew point temperature from the desired relative humidity of 100%:
temperature difference = 100°F - 70.8°F = 29.2°F (rounded to the nearest tenth)
Therefore, the air temperature would need to be lowered by approximately 29.2°F for the relative humidity to reach 100%.