If air at sea level with a temperature of 27degrees C is forced up a mountain slope and the air's dew point at the condensation level is 14degrees C, at what elevation will condensation begin?
Well, when air is forced up a slope, it's like giving it a little exercise. And just like us, when we exercise, we start to sweat. In this case, the air starts to condense. So, when the air temperature is 27 degrees C at sea level and the dew point is 14 degrees C, we have a difference of 13 degrees C. For every 1000 meters you climb, the air temperature drops about 6.5 degrees C. So, to find the elevation at which condensation begins, we'll divide the difference in temperature (13 degrees) by the rate of temperature change (6.5 degrees per 1000 meters). And don't worry, I'll do the math for you!
(13 degrees C) / (6.5 degrees C/1000 meters) = 2000 meters
So, at an elevation of 2000 meters, the air will start to condense. It's like the air saying, "I think it's time for a cloud workout!"
To determine the elevation at which condensation will begin, we need to calculate the difference in temperature between the air temperature and the air's dew point temperature.
Step 1: Convert the temperatures to Kelvin
Convert the air temperature from Celsius to Kelvin by adding 273.15:
Temperature = 27°C + 273.15 = 300.15 K
Convert the dew point temperature from Celsius to Kelvin:
Dew Point = 14°C + 273.15 = 287.15 K
Step 2: Calculate the temperature difference
Temperature difference = Air temperature - Dew point temperature
Temperature difference = 300.15 K - 287.15 K = 13 K
Step 3: Determine the lapse rate
The lapse rate represents the decrease in temperature with increasing elevation. The average value for the lapse rate is 6.5°C per 1000 meters (or 9.8°F per 1000 feet).
Step 4: Calculate the elevation
To calculate the elevation at which the condensation will begin, divide the temperature difference by the lapse rate and convert it to meters:
Elevation = (Temperature difference / Lapse rate) * 1000 m
Elevation = (13 K / 6.5°C per 1000 m) * 1000 m = 2000 meters
Therefore, condensation will begin at an elevation of 2000 meters.
To determine the elevation at which condensation will begin, we need to understand the concept of the dew point and how it relates to temperature and elevation. The dew point is the temperature at which air becomes saturated, meaning it holds as much moisture as it can. When the air temperature drops below the dew point, moisture begins to condense, forming dew, clouds, or other forms of precipitation.
To calculate the elevation at which condensation will begin, we need to utilize the concept of the lapse rate. The lapse rate describes the decrease in temperature with increasing elevation. Typically, the average lapse rate in the troposphere is around 6.5 degrees Celsius per kilometer (or 3.5 degrees Fahrenheit per 1,000 feet).
In this scenario, we have the following information:
- Initial air temperature at sea level: 27 degrees Celsius
- Dew point temperature: 14 degrees Celsius
First, we need to calculate the temperature difference between the air temperature at sea level and the dew point temperature. Subtracting the dew point temperature (14 degrees Celsius) from the air temperature at sea level (27 degrees Celsius), we find a temperature difference of 13 degrees Celsius.
Next, we divide this temperature difference by the lapse rate (6.5 degrees Celsius per kilometer) to find the change in elevation. Therefore, 13 degrees Celsius divided by 6.5 degrees Celsius per kilometer equals 2 kilometers. This means that for every 2 kilometers (or 2,000 meters) increase in elevation, the air temperature decreases by 13 degrees Celsius.
Hence, condensation will begin at an elevation of 2 kilometers above sea level in this scenario.
The decrease in temperature with rising altitude is 6.49 °C/1,000 m, according to ICAO definition, see:
http://en.wikipedia.org/wiki/Lapse_rate
Thus, to reach the dew point, the air mass must decrease (27-14)=13 degrees C, which translates to a rise in altitude of
(13 degrees C)/(6.49 degrees C / 1000 m)
= 2003 m
= 2000 m approximately
assuming no loss or gain in humidity of the air mass.