Fundamentals of Physical Geography
Fundamentals of Physical Geography
2nd Edition
ISBN: 9781133606536
Author: James Petersen
Publisher: CENGAGE L
Question
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Chapter 5, Problem 2PA

(a)

To determine

The height of the LCL if the air parcel has a temperature of 25°C and dew point temperature of 14°C and the temperature of the air parcel if it rises to 4,000 meters.

(a)

Expert Solution
Check Mark

Answer to Problem 2PA

The height of the Lifting Condensation Level (LCL) is 1375meters, and the temperature of air parcel that is at 4000 meters is - 1.9°C.

Explanation of Solution

The height of an air parcel at which the condensation begins is termed as Lifting Condensation Level (LCL). The formula to determine the LCL is as follows:

Lifting Condensation Level=125meters×(Celcius temperatureCelcius dew point)

Substituting the values of Celsius temperature as 25°C and Celsius dew point as 14°C,

LiftingCondensationLevel=125meters×(Celcius temperatureCelcius dew point)=125meters(2514)=125meters(11)=1375meters

To identify the temperature of air parcel at 4000meters,

Given info:

The temperature of the air parcel = 25°C

The height of the Lifting Condensation Level (LCL) =1375meters

To identify the distance between the starting point and the point of condensation, subtract the point of condensation with the starting point.

Distance between the starting point and the point of condensation} = The point of condensation - The starting point

Substituting the values 1375meters in the point of condensation and 0 meter in the starting point in the above expression,

Distance between the starting pointand the point of condensation} = 1375m - 0m                                                           = 1375m

Now, divide 1375meters by 100meters and multiply by 1°C. The reason for dividing by 100m and multiplying by 1°C is because the air parcel rises for every 100meters and the air temperature drops by 1°C.

1375meters100meters × 1°C = 13.75°C ----------------- (1)

Now, subtract the starting temperature (25°C) with the above temperature (13.75°C), as the above temperature is not the actual temperature at the point of condensation as it is in fact the total drop in temperature from the starting point to the point of the condensation level.

25°C - 13.75°C = 11.25°C

Therefore, the temperature at the point of condensation is 11.25°C.

Now, to determine the distance between the highest point (4000meters) and the LCL (1375meters),

4000meters - 1375meters = 2625meters

Now, divide 2625meters by 100meters and multiply by 0.5°C. The reason for dividing by 100m and multiplying by 0.5°C is because the air parcel rises for every 100meters after the point of condensation and the wet adiabatic lapse rate of 5°C for every 1000meters becomes operational, and the air temperature drops by 0.5°C for every100meters.

2625meters100meters × 0.5°C = 13.125°C -------------- (2)

Now, to identify the temperature of air parcel at 4000 meters,

 The temperature of air parcel at 4000 meters}= Starting temperature - [(Value at 1)+(Value at 2)] 

Substituting the value 25°C in the starting temperature and (1) and (2) values in the above expression,

 The temperature of air parcel at 4000 meters}=25°C - [(13.75°C)+(13.125°C)]                                          = 25°C - 26.895°C                                         = - 1.895  - 1.9°C

Therefore, the temperature of air parcel that is at 4000 meters is - 1.9°C.

(b)

To determine

The calculation of temperature and dew point temperature of an air parcel that has descended to 2,000 meters, which was previously at 6,000 meters having a temperature of –5°C and a dew point of –10°C.

(b)

Expert Solution
Check Mark

Answer to Problem 2PA

The temperature of the descending air parcel is 35°C, and the dew point temperature is 2°C.

Explanation of Solution

Given info:

The height of air parcel = 6000metersThe temperature of air parcel = -5°CThe dew point temperature = -10°C

The temperature of air parcel at 2000meters = ?

The general rule is that the temperature increases by 10°C for every 1000meters for a descending air parcel, and the dew point temperature increases by 2°C for every 1000meters.

Height of air parcel (in meters)Temperature (celsius)Dew point temperature (celsius)
6000510
500058
4000156
3000254
2000352

Therefore, the temperature of the descending air parcel is 35°C, and the dew point temperature is 2°C.

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