Assume that a parcel of air is forced to rise up and over a 6000-foot-high mountain. The initial temperature of the parcel at sea level is 76.5°F, and the lifting condensation level (LCL) of the parcel is 3000 feet. The DAR is 5.5°F/1000’ and the SAR is 3.3°F/1000’. Assume that condensation begins at 100% relative humidity and that no evaporation takes place as the parcel descends. Indicate calculated temperatures to one decimal point.
To solve this problem, we can follow these steps:
1. Determine the temperature at the lifting condensation level (LCL).
- The LCL is the level at which the parcel of air becomes saturated and condensation begins.
- Since the LCL is given as 3000 feet and the DAR is 5.5°F/1000’, we can calculate the temperature at the LCL as follows:
LCL temperature = initial temperature - (DAR x height of LCL in thousands of feet)
LCL temperature = 76.5°F - (5.5°F/1000’ x 3)
LCL temperature = 76.5°F - 16.5°F
LCL temperature = 60.0°F
2. Determine the temperature at the mountaintop.
- The mountaintop is 6000 feet high, so using the DAR, we can calculate the temperature at the mountaintop:
Mountaintop temperature = LCL temperature - (DAR x height of mountaintop in thousands of feet)
Mountaintop temperature = 60.0°F - (5.5°F/1000’ x 6)
Mountaintop temperature = 60.0°F - 33.0°F
Mountaintop temperature = 27.0°F
3. Determine the temperature at the base of the mountain.
- The base of the mountain is at sea level, so the temperature will be the same as the initial temperature:
Base temperature = 76.5°F
4. Determine the temperature after the parcel descends from the mountaintop to the base.
- The SAR tells us how the temperature changes during the descent.
Temperature change = SAR x height of the descent in thousands of feet
Temperature change = 3.3°F/1000’ x 6
Temperature change = 19.8°F (rounded to one decimal point)
- The temperature after the descent will be the initial temperature minus the temperature change:
Final temperature = Base temperature - temperature change
Final temperature = 76.5°F - 19.8°F
Final temperature ≈ 56.7°F (rounded to one decimal point)
Therefore, the final temperature of the air parcel after it descends from the mountaintop to the base will be approximately 56.7°F.