Answer :
Final answer:
The height of the cloud base when the temperature at the ground is 95 degrees F and the dew point is 85 degrees F is approximately 2000 feet. This estimation is made using the Dry Adiabatic Lapse Rate, which is calculated to be roughly 1850 feet, making option c) the closest answer.
Explanation:
The height of a cloud base can be estimated using the temperature and dew point by applying the Dry Adiabatic Lapse Rate (DALR), which is the rate at which temperature decreases with an increase in altitude for dry air, assumed at about 5.4 degrees Fahrenheit per 1000 feet. When the air temperature at the ground level is 95 degrees F and the dew point is 85 degrees F, we have a difference of 10 degrees F. For every 1000 feet we ascend, the air temperature decreases by 5.4 degrees F; this means it will take roughly 1000 feet for the temperature to decrease to the dew point.
To calculate the cloud base height, we divide the temperature difference by the lapse rate:
Temperature Difference: 95 degrees F - 85 degrees F = 10 degrees F
Lapse Rate: 5.4 degrees F/1000 feet
Height = Temperature Difference / Lapse Rate
Height = 10 degrees F / (5.4 degrees F/1000 feet) ≈ 1850 feet
Considering the options provided, the closest estimation for the height of the cloud base is 2000 feet, making option c) the correct answer.
