Air parcel w/temperature of 30 degrees celcius, dew point temperature of 21 degrees celcius is forced to go up

Question

from sea level in an atmosphere that has a temperature gradient of 8.5 degrees celcius per kilometer. if one stops to perform the force that forces the raising of the parcel for 500 meters, will it continue to go up? if yes, calculate what height will be created the base of the cloud.

Answer 1

This question is a little vague and confusing, but we'll try.  Think in terms of lifting a parcel on a tephigram or skew-T plot.

If you take the parcel and lift it assuming the parcel cools at a dry adiabatic lapse rate of 10 degrees per kilometer, after 500 meters the parcel will have cooled by 5 degrees to 25 degrees celsius.  

The surrounding atmosphere, however will have cooled at the lapse rate of 8.5 degrees per kilometer, and after 500 meters will have cooled by 4.25 degrees to 25.75 degrees celsius.

So the answer is no, the parcel will not continue to rise as it's temperature is less than that of the atmosphere and therefore it is not buoyant.

If we wished to keep pushing on that parcel, however, to create a cloud base, we would need the temperature to drop another 4 degrees in order for the dewpoint temperature to be reached and saturation to occur.  At a dry adiabatic lapse rate of 10 degrees per kilometer, or 1 degree per 100 meters, our parcel would have to rise another 400 meters for a total of 900 meters.  Therefore, our cloud base would reside at 900 meters given sufficient forcing to push that parcel up to the condensation level.