At 5000 feet above surface level the temperature is 46.5° F. What is the temperature at surface level using the environmental lapse rate?
A. 40.0° F
B. 29.0° F
C. 64.0° F
D. 70.5°F
Answer (1)
Calculate the temperature difference: The temperature difference is found by multiplying the altitude difference (5000 feet) by the environmental lapse rate (3.5° F per 1000 feet).
Find the temperature difference: 1000 5000 × 3.5 = 17.5 °F.
Add the temperature difference to the temperature at 5000 feet: 46.5 + 17.5 = 64.0 °F.
The temperature at surface level is \boxed{64.0} °F.
Explanation
Understanding the Problem We are given that the temperature at 5000 feet above surface level is 46.5° F. We need to find the temperature at surface level using the environmental lapse rate, which is 3.5° F per 1000 feet.
Calculating the Temperature Difference First, we need to calculate the temperature difference between 5000 feet and surface level. The environmental lapse rate tells us how much the temperature changes for every 1000 feet of altitude change.
Calculating the Temperature Difference (Detailed) The temperature difference is calculated as follows:
Temperature difference = (Altitude difference / 1000 feet) * Environmental lapse rate
Altitude difference = 5000 feet Environmental lapse rate = 3.5° F / 1000 feet
Temperature difference = 1000 feet 5000 feet × 3.5° F = 5 × 3.5° F = 17.5° F
Finding the Surface Temperature Since the temperature decreases as altitude increases, the temperature at the surface level will be higher than the temperature at 5000 feet. Therefore, we add the temperature difference to the temperature at 5000 feet to find the temperature at the surface level.
Calculating the Surface Temperature (Detailed) Temperature at surface level = Temperature at 5000 feet + Temperature difference
Temperature at 5000 feet = 46.5° F Temperature difference = 17.5° F
Temperature at surface level = 46.5° F + 17.5° F = 64.0° F
Final Answer Therefore, the temperature at surface level is 64.0° F.
Examples
Understanding the environmental lapse rate is crucial in various real-world applications. For example, pilots use this rate to estimate air temperature at different altitudes, which is essential for flight planning and safety. Similarly, meteorologists use the lapse rate to predict weather patterns and temperature changes in mountainous regions. This concept also helps in understanding climate variations and designing energy-efficient buildings by considering temperature changes with altitude.
